Optical apparatus

ABSTRACT

An optical apparatus has an imaging optical system provided with a deformable mirror and an electronic zoom function that an image recorded in an image sensor by the imaging optical system is magnified by image processing. A ray deflecting function of the deformable mirror is changed in accordance with a change of an object area corresponding to an image to be used, and aberration of the imaging optical system is optimized. The deformable mirror is controlled by an arithmetical unit connected to an image processor and a driving circuit. The electronic zoom is performed with respect to the image recorded in the image sensor through a signal processing circuit and the image processor, and when the image is displayed on a display device, the deformable mirror is deformed so that sharpness at nearly the center of an object image formed on the image sensor is improved. This offers the optical apparatus in which a compact design is achieved, the magnification of the optical system can be changed, and the sharpness of the image is high even when a variable magnification ratio is increased.

This is a divisional of U.S. application Ser. No. 10/775,340, filed Feb.11, 2004 (issue fee paid), which, in turn, relies for priority uponJapanese Patent Application No. 2003-035430, filed Feb. 13, 2003, thecontents of both of which are incorporated herein by reference in theirentireties.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates to an optical apparatus for obtaining an imageused by a user.

2. Description of Related Art

In the optical apparatus of this type, there has been the need that auser wants to observe in detail or magnify only a particular part of animage of an object should be observed in detail or magnified. Inresponse to this, for example, in an imaging apparatus such as a digitalcamera or a TV camera, optical zoom or electronic zoom (also calleddigital zoom) has been used as the technique meeting the above need. Thetechnique of the electronic zoom is set forth, for example, in JapanesePatent Kokai No. 2002-320135.

In a telescope, the magnification of an optical system has been changedby the replacement of an eyepiece to thereby meet the above need. In amicroscope, an objective lens has been replaced to thereby satisfy theabove need.

An optical apparatus using the electronic zoom, for example, the digitalcamera, is designed so that an image photographed and stored through animaging optical system at the center of the imaging surface of an imagesensor inside the digital camera is magnified by an image processor andis processed with respect to pixel interpolation. The image is thusdisplayed or output to a display device.

In the telescope or the microscope, when the eyepiece or the objectivelens is replaced, combined aberration of the entire optical system ischanged.

SUMMARY OF THE INVENTION

The optical apparatus according to the present invention has an opticalsystem provided with a variable optical-property element so that a raydeflecting function of the variable optical-property element is changedin accordance with a change of an object area corresponding to an imageto be used and aberration of the optical system is optimized.

The optical apparatus according to the present invention has a variableoptical-property element, a driving circuit driving the variableoptical-property element, and an electronic zoom function.

The optical apparatus according to the present invention preferably hasat least two optical element units and at least one of the opticalelement units is changed in the electronic zoom.

The optical apparatus according to the present invention is a variablemagnification optical apparatus that has the optical system providedwith the variable optical-property element, in which the ray deflectingfunction of the variable optical-property element is changed inaccordance with the magnification change of the optical system, andthereby aberration of the optical system changed in accordance with themagnification change is optimized.

The optical apparatus according to the present invention uses acombination of a plurality of optical units, one of which is providedwith the variable optical-property element, so that the ray deflectingfunction of the variable optical-property element is changed inaccordance with a variation of the combination, and thereby aberrationof the optical system changed in accordance with the variation isoptimized.

The optical apparatus according to the present invention includes aplurality of optical units, one of which is provided with the variableoptical-property element, so that the ray deflecting function of thevariable optical-property element is changed in accordance with themagnification change of the optical system, and thereby aberration ofthe optical system changed in accordance with the magnification changeis optimized.

According to the present invention, the optical apparatus is any one ofan observing apparatus, a telescope, a microscope, and an endoscope.

According to the present invention, the variable optical-propertyelement is a variable focal-length lens or a variable mirror.

The optical apparatus according to the present invention is providedwith an electronic zoom function so that a certain part of the opticalsystem is changed in the electronic zoom, and thereby the imagesharpness of an image area used in the electronic zoom is improved.

The optical apparatus according to the present invention has a variableoptical-property element, a driving circuit driving the variableoptical-property element, and an electronic zoom function. When theelectronic zoom is performed, the variable optical-property element isdriven so that the image sharpness of the image area magnified by theelectronic zoom of the optical system including the variableoptical-property element becomes best.

The optical apparatus according to the present invention has a variableoptical-property element, a driving circuit driving the variableoptical-property element, and an electronic zoom function. When theelectronic zoom is performed, the variable optical-property element isdriven so that the image sharpness of the image area magnified by theelectronic zoom of the optical system including the variableoptical-property element becomes best, taking account of a change of animaging state caused by at least one of a change of an object distance,temperature, humidity, a manufacturing error, a change with age,vibration, and an optical magnification change.

The optical apparatus according to the present invention has a variableoptical-property element, a driving circuit driving the variableoptical-property element, and an electronic zoom function. When theelectronic zoom is performed, the variable optical-property element isdriven so that the image sharpness of the image area magnified by theelectronic zoom of the optical system including the variableoptical-property element becomes best, taking account of themanufacturing error of the optical apparatus.

The optical apparatus according to the present invention has a variableoptical-property element, a driving circuit driving the variableoptical-property element, driving information, an image sensor, and anelectronic zoom function. When the electronic zoom is used to form animage, the variable optical-property element is driven so thataberration of the image of the image area magnified by the electroniczoom of the optical system including the variable optical-propertyelement is reduced.

According to the present invention, the optical system including thevariable optical-property element is a single focal-length opticalsystem or a zoom optical system.

The optical apparatus according to the present invention preferably hasan autofocus function.

The optical apparatus according to the present invention is designed toform an image while changing driving information provided to thevariable optical-property element, to find the driving information thatthe focus or contrast of a formed image becomes nearly best, and todrive the variable mirror through the driving information.

The optical apparatus according to the present invention preferably hasan image shake correcting function.

The optical apparatus according to the present invention has a variableoptical-property element, a driving circuit driving the variableoptical-property element, at least one optical element unit, and anelectronic zoom function. When the electronic zoom is performed, thevariable optical-property element and the optical element unit areassociated with each other to thereby improve the sharpness of the imagearea used in the electronic zoom.

The optical apparatus according to the present invention is such thatthe electronic zoom is performed and, at the same time, a stop is open.

The optical apparatus according to the present invention is such that anelectronic zoom magnification satisfies the following condition in acertain state:1.05<β_(E)<30×√{square root over ((M/10⁶))}where β_(E) is the electronic zoom magnification and M is the number ofpixels of an image sensor.

The optical apparatus according to the present invention is such thatthe number of pixels of the image sensor satisfies the followingcondition:M≧two hundred thousand

The optical apparatus according to the present invention has atelephonic function.

The optical apparatus according to the present invention is preferably amobile phone.

The optical apparatus according to the present invention has an imagedisplay function.

The optical apparatus according to the present invention is such thatwhen the electronic zoom is performed, at least one of the opticalelement units is moved and thereby the sharpness of a part of an imageto be used is improved.

The optical apparatus according to the present invention is providedwith an image sensor so that a stop is open in the electronic zoom.

According to the present invention, the optical apparatus in which acompact design is achieved, the magnification of the optical system canbe changed, and even when a variable magnification ratio is increased,an image with high sharpness is obtained can be provided.

These and other features and advantages of the present invention willbecome apparent from the following detailed description of the preferredembodiments when taken in conjunction with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a view schematically showing a first embodiment of the opticalapparatus according to the present invention;

FIG. 2 is an explanatory view showing the relationship between animaging surface of an image sensor and an image to be formed in theoptical apparatus;

FIGS. 3A and 3B are explanatory views showing examples of data in anLUT;

FIG. 4 is an explanatory view showing the relationship between theimaging surface of the image sensor and the image to be formed in theoptical apparatus;

FIG. 5 is a view schematically showing a second embodiment of theoptical apparatus according to the present invention;

FIG. 6 is a view schematically showing a third embodiment of the opticalapparatus according to the present invention;

FIG. 7 is a view schematically showing a fourth embodiment of theoptical apparatus according to the present invention;

FIG. 8 is a view schematically showing a fifth embodiment of the opticalapparatus according to the present invention;

FIG. 9 is a Y-Z sectional view showing the first embodiment of anoptical system applicable to the optical apparatus of the presentinvention;

FIG. 10 is a diagram showing transverse aberration characteristics atthe infinity of an object point distance of the optical system of FIG.9;

FIG. 11 is a diagram showing transverse aberration characteristics at anobject point distance of 150 mm in the first embodiment;

FIG. 12 is a graph showing a wave optical MTF (140 lines/mm) at 9.67° inthe −Y direction of the object (which refers to the orientation of theobject where X is 0.000° and Y is −9.67°) when twofold electronic zoomis performed by the optical system of the first embodiment, optimizingthe configuration of a thin film so that when the size of the imagingsurface of the image sensor is assumed as 2 mm×1.5 mm, the sharpness ofthe image is improved in this area at the infinity of the object pointdistance;

FIG. 13 is a graph showing a wave optical MTF (140 lines/mm) at 9.67° inthe −Y direction of the object (which refers to the orientation of theobject where X is 0.000° and Y is −9.67°) when twofold electronic zoomis performed by the optical system of the first embodiment, optimizingthe configuration of the thin film so that when the size of the imagingsurface of the image sensor is assumed as 2 mm×1.5 mm, the sharpness ofthe image is improved in this area at an object point distance of 150mm;

FIG. 14 is a graph showing the MTF where the configuration of the thinfilm is not optimized in the optical system of the first embodiment, atthe infinity of the object point distance where the size of the imagingsurface is 4 mm×3 mm;

FIG. 15 is a graph showing the MTF where the configuration of the thinfilm is not optimized in the optical system of the first embodiment, atan object point distance of 150 mm where the size of the imaging surfaceis 4 mm×3 mm;

FIG. 16 is a Y-Z sectional view schematically showing the secondembodiment, at a wide-angle position, of an optical system applicable tothe optical apparatus of the present invention;

FIG. 17 is a Y-Z sectional view schematically showing the secondembodiment, at a middle position, of the optical system applicable tothe optical apparatus of the present invention;

FIG. 18 is a Y-Z sectional view schematically showing the secondembodiment, at a telephoto position, of an optical system applicable tothe optical apparatus of the present invention;

FIG. 19 is a graph showing the MTF where twofold electronic zoom isperformed in the optical system of the second embodiment of FIGS. 16-18;

FIG. 20 is a graph showing the MTF where the configuration of thevariable mirror is optimized with respect to only a part of the imageused when the electronic zoom is performed in the optical system of thesecond embodiment of FIGS. 16-18;

FIG. 21 is a diagram schematically showing an example of a deformablemirror as a variable optical-property element applicable to the opticalsystem used in the optical apparatus of the present invention;

FIG. 22 is a diagram schematically showing another example of thevariable mirror;

FIG. 23 is an explanatory view showing one aspect of electrodes used inthe variable mirror of FIGS. 21 and 22;

FIG. 24 is an explanatory view showing another aspect of electrodes usedin the variable mirror of FIGS. 21 and 22;

FIG. 25 is a view schematically showing another example of the variablemirror;

FIG. 26 is a view schematically showing another example of the variablemirror;

FIG. 27 is a view schematically showing another example of the variablemirror;

FIG. 28 is an explanatory view showing the winding density of athin-film coil in the example of FIG. 27;

FIG. 29 is a view schematically showing another example of the variablemirror;

FIG. 30 is an explanatory view showing one example of an array of coilsin the example of FIG. 29;

FIG. 31 is an explanatory view showing another example of the array ofcoils in the example of FIG. 29;

FIG. 32 is an explanatory view showing an array of permanent magnetssuitable for the array of coils of FIG. 31 in the example of FIG. 27;

FIG. 33 is a view schematically showing the variable mirror applicableto the optical apparatus of the present invention;

FIG. 34 is a view schematically showing the variable mirror in which afluid is taken in and out by a micropump to deform a lens surface;

FIG. 35 is a view schematically showing one example of the micropump;

FIG. 36 is a view showing the principle structure of a variablefocal-length lens applicable to the optical system of the presentinvention;

FIG. 37 is a view showing the index ellipsoid of a nematic liquidcrystal of uniaxial anisotropy;

FIG. 38 is a view showing a state where an electric field is applied toa macromolecular dispersed liquid crystal layer in FIG. 36;

FIG. 39 is a view showing an example where a voltage applied to themacromolecular dispersed liquid crystal layer in FIG. 36 can be changed;

FIG. 40 is a view showing an example of an imaging optical system fordigital cameras which uses the variable focal-length lens in the opticalapparatus of the present invention;

FIG. 41 is a view showing an example of a variable focal-lengthdiffraction optical element applicable to the optical system of theoptical apparatus of the present invention;

FIG. 42 is a view showing variable focal-length spectacles, each havinga variable focal-length lens which uses a twisted nematic liquidcrystal;

FIG. 43 is a view showing the orientation of liquid crystal moleculeswhere a voltage applied to a twisted nematic liquid crystal layer ofFIG. 42 is increased;

FIGS. 44A and 44B are views showing two examples of variabledeflection-angle prisms applicable to the optical system of the opticalapparatus of the present invention;

FIG. 45 is a view for explaining the applications of the variabledeflection-angle prisms shown in FIGS. 44A and 44B;

FIG. 46 is a view schematically showing an example of a variablefocal-length, mirror which functions as the variable focal-length lensapplicable to the optical system of the optical apparatus of the presentinvention;

FIG. 47 is a view schematically showing an imaging optical system whereanother example of the variable focal-length lens is used in the opticalsystem of the optical apparatus of the present invention;

FIG. 48 is an explanatory view showing a modified example of thevariable focal-length lens of FIG. 47;

FIG. 49 is an explanatory view showing a state where the variablefocal-length lens of FIG. 48 is deformed;

FIG. 50 is a view schematically showing another example of the variablefocal-length lens, applicable to the optical system of the opticalapparatus of the pre-sent invention, in which a fluid is taken in andout by the micropump to deform a lens surface;

FIG. 51 is a view schematically showing another example of the variableoptical-property element, applicable to the optical system of theoptical apparatus of the present invention, which is the variablefocal-length lens using a piezoelectric substance;

FIG. 52 is an explanatory view showing a state where the variablefocal-length lens of FIG. 51 is deformed;

FIG. 53 is a view schematically showing still another example of thevariable optical-property element, applicable to the optical system ofthe optical apparatus of the present invention, which is the variablefocal-length lens using two thin plates constructed of piezoelectricsubstances;

FIG. 54 is a view schematically showing still another example of thevariable focal-length lens applicable to the optical system of theoptical apparatus of the pre-sent invention;

FIG. 55 is an explanatory view showing the deformation of the variablefocal-length lens of FIG. 54;

FIG. 56 is a view schematically showing a further example of thevariable optical-property element, applicable to the optical system ofthe optical apparatus of the present invention, which is the variablefocal-length lens using a photonical effect;

FIGS. 57A and 57B are explanatory views showing the structures oftrans-type and cis-type azobenzene, respectively, used in the variablefocal-length lens in FIG. 56;

FIG. 58 is a view schematically showing another example of the variablemirror applicable to the optical system of the optical apparatus of thepresent invention;

FIGS. 59A and 59B are a side view showing an electromagnetic drivingvariable mirror applicable to the optical system of the opticalapparatus in the aspect of the present invention and a view looking fromthe opposite side of a reflection film, respectively;

FIG. 60 is a view schematically showing a conventional example of aNewtonian reflecting telescope;

FIG. 61 is a view schematically showing a reflecting telescope using thedeformable mirror which is the optical apparatus according to thepresent invention; and

FIG. 62 is a view schematically showing a microscope using the variablefocal-length lens which is also the optical apparatus according to thepresent invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

FIG. 1 shows the first embodiment of the optical apparatus of thepresent invention. In this embodiment, an optical apparatus 302 has animaging optical system 301 provided with a variable mirror 409 as thevariable optical-property element and an electronic zoom function thatan image recorded in a recording element, such as the image sensor, bythe imaging optical system 301 is magnified by image processing.

The electronic zoom, also called digital zoom, as set forth, forexample, in Kokai No. 2002-320135, is adapted to perform zoom processingin a preset direction with respect to image data stored in a memory sothat a plurality of pixels are allocated to addresses.

The imaging optical system 301 includes, in order from the object side,a concave lens 309, the variable mirror 409, an aperture stop 521, aconvex lens 901 a, a convex lens unit 902 a with two lens componentscomposed of three lens elements, and a filter unit 301 a, having alow-pass filter and/or an infrared cutoff filter, which does not affectimaging performance.

The imaging optical system is a single focal-length optical system andis constructed so that when an object distance is changed by thedeformation of a thin film 409 a constituting the reflecting surface ofthe variable mirror 409, focusing can be carried out.

The variable mirror 409, which includes a deformable three-layerstructure supported on the upper surface of an annular support 423, hasa thin film 409 a whose surface layer constitutes a reflecting surface,an intermediate substrate 409 j holding the thin film 409 a, a thinlower-layer electrode 409 k, and a plurality of electrodes 409 barranged at preset intervals with respect to the electrode 409 k on thelower side of the support 423. The electrode 409 k and the plurality ofelectrodes 409 b are connected to a driving circuit 304 provided withvoltage-controllable, variable resistors so that preset voltages areselectively applied between the electrode 409 k and the plurality ofelectrodes 409 b to deform the thin film 409 a.

The driving circuit 304 is connected to an arithmetical unit 414 whichcalculates the configuration of the thin film 409 a subjected todeformation in the electronic zoom, that is, the position and the amountof deformation of the thin film 409 a and outputs a control signal inaccordance with the result of the calculation. A temperature sensor 415securing the working ambient data of the optical apparatus, a humiditysensor 416, and a range sensor 417 are connected to the arithmeticalunit 414.

The electronic zoom is performed through a signal processing circuit 308which acquires a pixel signal by timing from individual pixels(light-receiving elements) constituting the imaging surface of an imagesensor 408 to process the signal so that a real time moving image of theobject formed on the imaging surface of the image sensor 408 by theimaging optical system 301 is displayed on a display device 306, animage processor 303 which processes data signal-processed by the signalprocessing circuit 308 so that the data are displayed as a magnifiedimage on the display device 306, and the arithmetical unit(microprocessor) 414 which calculates the control signal deforming thereflecting surface of the variable mirror 409 so that the control signalsuch as to acquire the pixel signal by timing with respect to the signalprocessing circuit 308 is output and focusing of the imaging opticalsystem 301 and the sharpness of the image at nearly the center of theimaging surface are improved in a focus state of the magnified imagewhere the image is processed by the image processor 303.

The arithmetical unit 414 is provided with a calculating means formaking calculations in the electronic zoom and a calculating means formaking calculations to control the shape of the variable mirror 409 inaccordance with a signal from the above calculating means and signalsfrom the sensors 415, 416, and 417.

The variable mirror 409 is thus constructed so that it is controlled bythe arithmetical unit 414 connected to the image processor 303 and thedriving circuit 304. In order to perform the electronic zoom withrespect to the image recorded in the image sensor 408 through the signalprocessing circuit 308 and the image processor 303 and to heighten thesharpness at nearly the center of an object image (an image of theobject to be photographed) formed on the image sensor 408 when the imageis displayed on the display device 306, the variable mirror 409 isdriven through the driving circuit 304, including the case of focusing,so that the thin film 409 a constituting the reflecting surface of thevariable mirror 409 is deformed.

In addition to being displayed on the display device 306, the imageprocessed by the image processor 303 can be printed by a printer 307 andcan also be recorded and stored in a memory 305. In the firstembodiment, the sensors 415, 416, and 417 and the printer 307 need notnecessarily be provided.

FIG. 2 shows the relationship between the imaging surface of the imagesensor and the image to be formed. In a conventional imaging apparatus,when ordinary electronic zoom is performed, only a center portion 312 ofan imaging surface 311 of the image sensor 408 is displayed as an imageon the display device 306 such as that shown in FIG. 1, is printedthrough the printer 307, or is stored in the memory 306. This image ismagnified by the image processor 303 and is processed with respect topixel interpolation. The image is thus output to the display device. Inthis state, however, aberration produced in the imaging optical system301 for forming the image of an object 314 on the image sensor 408 alsobecomes a magnified image, and hence there is the drawback that theimage is blurred.

Thus, the first embodiment shown in FIG. 1, when performing theelectronic zoom, is provided with a control means for controlling theshape of the thin film 409 a constituting the reflecting surface wherethe image is formed on the imaging surface 311 of the image sensor 408so that aberration of the image of the center portion 312 of the imagingsurface 311 is reduced. In this case, aberration of the image of theoutside area of the center portion 312 may be deteriorated. This isbecause, in most cases, the image of the outside area is not displayednor stored. However, control may, of course, be made so that theaberration of the outside area of the center portion 312 is corrected.

As a specific control means, for example, a look-up table (hereinafterabbreviated to LUT) such as that shown in each of FIGS. 3A and 3B isused. Each of FIGS. 3A and 3B shows an example of data matrix in theLUT.

The LUT of this embodiment is the data matrix in which the column titleis the object distance (photographing distance) from the first surfaceon the object side of the imaging optical system 301 in the opticalapparatus of FIG. 1 to the object 314 and the row title is the electrodenumber of the electrodes 409 b. Numerical values in the LUT of eachfigure are the ones of voltages applied between the electrodes 409 b andthe electrode 409 k at individual object distances. The voltages areexpressed in volts. The LUT is stored in a LUT data section 313 of theoptical apparatus in FIG. 1.

The LUT data section 313 is controlled so that when the electronic zoomis not performed, the data of the LUT of FIG. 3A are used, while whenthe electronic zoom is performed, the data of the LUT of FIG. 3B areused.

In the data of the LUT of FIG. 3A, the voltages are set so that the thinfilm 409 a is deformed and thereby aberration of the image on the entireimaging surface 311 of the image sensor 408 is reduced, whereas in thedata of the LUT of FIG. 3B, the voltages are set so that the thin film409 a is deformed and thereby aberration of the image of the centerportion 312 on the imaging surface 311 is reduced.

In the optical apparatus of the present invention, the LUTs constructedas mentioned above are used, and thus even when the electronic zoom isperformed, an image with high sharpness can be photographed, displayed,and stored.

Also, the far-point allowance and the near-point allowance in FIGS. 3Aand 3B are values used for the purpose that when photo-focusing of ahill-climbing method (or called a contrast method) takes place, an imageis first brought to a considerably out-of-focus state to find a positionwhere the contrast of the image is low and then to determine a positionwhere the contrast of the image is maximized while scanning the LUT fromthe above state and gradually changing focusing.

In the optical apparatus of FIG. 1, since an electrostatic drivingvariable mirror is used as the variable mirror 409, the values in theLUT are indicated by the voltages, but an electromagnetic drivingvariable mirror may be used. In this case, it is merely necessary thatthe values in the LUT are indicated by electric currents flowing throughindividual electrodes. Also, in the present invention, the value of thevoltage or electric current used for driving the thin film 409 isreferred to as driving information.

Although the optical apparatus of FIG. 1 is constructed to use thevariable mirror 409, the present invention is not limited to thisconstruction, and a zoom operation may be performed by a combination ofa variable optical-property element which can change aberration, such asa variable focal-length lens or a variable prism, and the electroniczoom.

The variable focal-length lens is shown, for example, in FIG. 36. In avariable focal-length lens 511 of FIG. 36, when an electrode 513 a or anelectrode 513 b is divided into a plurality of electrodes, aberration ofthe image used as a picture, like the optical apparatus of FIG. 1, canbe reduced.

The optical apparatus of the first embodiment may be constructed so thatnumerical values derived from the LUTs of FIGS. 3A and 3B areinterpolated to obtain the optimum driving information.

When the values in the LUTs of FIGS. 3A and 3B are determined, thedesign values of the imaging optical system 301 may be used, butalternatively, the values in the LUTs may be determined so that when theoptical apparatus 302 is fabricated, aberration or the MTF of the imageformed by the imaging optical system 301 becomes best, including thefabrication error. By doing so, an optical apparatus with a higherdegree of accuracy than the case where only the design values are usedto determine the values in the LUTs can be provided.

Specifically, it is only necessary that, for example, the test chart 314provided as the object is placed at each of some object distances and isimaged by the optical apparatus 302, and after the values of the LUTsare determined so that the contrast of the test chart 314 placed at eachdistance is optimized in cases where the electronic zoom is performedand not, the values are stored in the LUT data section 313.

The optical apparatus of the first embodiment may also be constructed sothat, for example, the LUT is used to improve imaging performance wherethe electronic zoom takes place, with respect to the degradation ofimaging performance of the optical apparatus attributable to changes intemperature and humidity, a change with age, and an image shake causedby an unsteady hold and vibrations.

For image shake compensation, it is only necessary that the shake of theoptical apparatus is detected by a shake sensor 424 connected to thearithmetical unit 414, and the thin film 409 a is deformed through thedriving circuit 304 so that the shake is canceled. In addition, it isonly necessary to provide driving information for shake compensation tothe image processor 303.

In the optical apparatus of FIG. 1, the imaging optical system 301 isconstructed as a single focal-length optical system, but it can be doneas a zooming optical system. In this case, the optical apparatus with ahigher zoom ratio, in addition to the electronic zoom, is obtained.However, when the imaging optical system 301 is constructed as thezooming optical system, the mechanical size of the optical apparatus isincreased. In this case also, by using the LUTs as an aberrationcompensating means in the electronic zoom, as described with referenceto FIGS. 2, 3A, and 3B, an image with high sharpness is obtained.

It is only necessary that, in addition to the data shown in FIGS. 3A and3B, the LUTs in this case possess data provided with the drivinginformation in FIGS. 3A and 3B in accordance with optical zoom states attelephoto, middle, and wide-angle positions of the optical system.Alternatively, the optical apparatus may be designed so that when theelectronic zoom is performed at only the telephoto position in theoptical zoom, the LUTs possess data provided with the drivinginformation in FIGS. 3A and 3B at only the telephoto position.

When the electronic zoom is performed with a plurality of kinds ofmagnification, the LUTs may possess data groups provided with thedriving information in FIGS. 3A and 3B in accordance with the kind ofmagnification. For example, in order to perform the electronic zoom withfour kinds of magnification, it is only necessary to possess data groupsprovided with four kinds of driving information.

As an area magnified by the electronic zoom, not only the middle portionof an imaging area indicated as the center portion 312 of the imagingsurface 311 in FIG. 2, but also, for example, as shown in FIG. 4, anarbitrary portion such as one portion 315 of the imaging surface 311divided into four can be used. In this case, it is only necessary that,by possessing the data provided with the driving information in FIGS. 3Aand 3B, the variable mirror 409 is controlled so that aberrationproduced by the imaging optical system 301 in the area of the portion315 is reduced.

Subsequently, a description will be given of the electronic zoommagnification. If the electronic zoom magnification is too high, animage becomes rough, which is unfavorable. If it is too low, the effectof adoption on the electronic zoom will not be obtained. Here, when thenumber of pixels is represented by M and the electronic zoommagnification is represented by β_(E), it is desirable that theelectronic zoom magnification β_(E) satisfies the following condition:1.05<β_(E)<30×√{square root over ((M/10⁶))}  (1)

The upper limit of Condition (1) is proportional to √{square root over(M)}, because even when the image is magnified as the number of pixelsis increased, the roughness of the image becomes invisible.

When the following condition is satisfied, the roughness of the image isinvisible and the efficiency of image magnification is increased, whichis favorable.1.1<β_(E)<15×√{square root over ((M/10⁶))}  (1′)

When the following condition is further satisfied, an image whoseroughness is hard to see even in printing is obtained, which isfavorable.M≧two hundred thousand  (2)

In the optical apparatus of FIG. 1, when the imaging optical system 301is pan-focus, that is, in the case where focus adjustment is unnecessaryeven though the object distance is varied, the variable mirror 409 canbe controlled for only the purpose of correcting aberration in theelectronic zoom. In this case, the data provided with the drivinginformation of the LUTs in FIGS. 3A and 3B are such that the number ofvariable values in the column title is decreased to 1 or close to 1.

In the optical apparatus of the first embodiment, it is convenient toprovide a telephonic function 316, such as a mobile phone, to theoptical apparatus 302. The optical apparatus 302 of this embodiment maybe incorporated in the mobile phone. This is very favorable becausephotographing is performed by a compact apparatus in which zoom ispossible, and an image with high sharpness is obtained.

FIG. 5 shows the second embodiment of the present invention. The opticalapparatus 302 of the second embodiment has the same structure as that ofthe first embodiment with the exception of the imaging optical system301. Specifically, the imaging optical system 301 of the secondembodiment includes, in order from the object side, the concave lens309, the variable mirror 409, the aperture stop 521, a convex lens 901,a convex lens unit 902 with one lens component composed of two lenselements, and a convex lens 310.

The variable mirror 409 used in the optical apparatus 302 of the secondembodiment, an arithmetical control means for controlling the shape ofthe thin film 409 a of the variable mirror 409, and an electronic zoomdisplay means for magnifying and displaying the object image formed onthe imaging surface of the image sensor by performing the electroniczoom are identical with those of the first embodiment, and thus theirexplanation is omitted. The optical apparatus of the second embodimentbrings about the same effect as that of the first embodiment.

FIG. 6 shows the third embodiment of the present invention. An opticalapparatus 321 of the third embodiment, in which the imaging opticalsystem is constructed as a zooming optical system 320, has the samestructure as the optical apparatus 302 of the first embodiment with theexception of the imaging optical system. The optical apparatus 321 ofthe third embodiment is constructed by combining the zooming opticalsystem 320 with the electronic zoom described in the first embodiment.Also, the same parts as in the optical apparatus of the firstembodiment, that is, the signal processing circuit 308, the drivingcircuit 304, etc., are omitted from FIG. 6.

The zooming optical system 320 includes, in order from the object side,a concave lens 322, the variable mirror 409, a lens unit 323, a fixedlens unit 324, the aperture stop 521, a lens unit 325, and a lens unit326. The lens unit 323 is a variable magnification lens unit and thelens unit 325 is a compensator. They are designed to move along theoptical axis (in the directions of arrows in FIG. 6) in the zoomoperation. The variable mirror 409 is constructed to perform focusingwhere the object distance is changed and to correct a focus shift whichcannot be completely corrected by the compensator 325 in the zoomoperation. When the lens unit 326 is designed to be movable along theoptical axis together with the lens units 323 and 325, usefulness to bedescribed later is obtained. These lens units 323, 325, and 326 aredriven through a driving device 327 controlled by the arithmetical unit414.

In the optical apparatus 321 of the third embodiment, as well as in theoptical apparatus 302 of the first embodiment, when the electronic zoomis performed, the shape of the thin film 409 a is optimized and theimage is formed so that the sharpness of the area used as the image inthe image sensor is improved.

The optical apparatus 321 of the third embodiment may be constructed sothat the variable mirror 409 is replaced with a mirror whose shape isnot changed and the lens unit 326 is moved along the optical axis (inthe directions of arrows of the FIG. 6), thereby improving the sharpnessof the area used as the image where the electronic zoom is performed.That is, when it is designed so that the three lens units 323, 325, and326 can be moved, the degree of freedom for adjusting aberration can beprovided in addition to the magnification change and correction for thefocus shift caused by the magnification change. Consequently, when theelectronic zoom is performed, the lens units 323, 325, and 326 aretogether moved along the optical axis, and thereby an image which ishigh in sharpness can be obtained.

Also, when the optical apparatus 321 of the third embodiment, as shownin FIG. 6, is provided with the variable mirror 409, at least one of thelens unit 325 constituting the compensator, the lens unit 326, and thelens unit 323 constituting the variable magnification lens unit is movedalong the optical axis (in the directions of arrows of FIG. 6) whilechanging the shape of the variable mirror 409. Whereby, the optical zoommagnification is maintained to have a necessary value so that thesharpness of only the image used by the electronic zoom is improvedwhile bringing the object into focus. The optical apparatus 321 may beconstructed as mentioned above. By doing so, the number of degrees offreedom of correction for aberration of the image is increased, and thusan image with high sharpness can be obtained.

FIG. 7 shows the fourth embodiment of the present invention. An opticalapparatus 331 of the fourth embodiment is constructed so that a mirror330 whose shape is not changed has the electronic zoom function. In thisoptical apparatus, two optical element units (a lens unit 332 and thelens unit 326) are together moved along the optical axis (in thedirections of arrows of FIG. 7). Whereby, the driving device 327 iscontrolled by the arithmetical unit 414 so as to make correction foraberration where the electronic zoom is performed and to carry outfocusing where the object distance is changed.

When the electronic zoom is performed, the lens units 332 and 336 aretogether moved along the optical axis (in the directions of arrows ofFIG. 7) in accordance with the object distance so that the sharpness ofonly the area used as the image in the image sensor 408 is improved.Whereby, the driving device 327 is controlled by the arithmetical unit414.

The optical apparatus 331 of the fourth embodiment, instead of using themirror 330 whose shape is not changed, shown in FIG. 7, may beconstructed to use the variable mirror 409 such as that shown in FIG. 1.In this case, one of the lens units 332 and 326 may be fixed. Thevariable mirror 409 and one of the lens units 332 and 326 are togetherdriven when the electronic zoom is performed, and thereby the sharpnessof the image of the area used in the electronic zoom can be improved.

When the pan-focus optical system is constructed, the focus positionneed not be corrected even when the object distance is changed, andhence one of the lens units 332 and 326 may be moved. In this case, itis only necessary that the focal length of the lens unit to be moved isset at nearly infinity.

The optical apparatus 331 of the fourth embodiment may also beconstructed to open the stop simultaneously with the start of theelectronic zoom in order to decrease the F-number of the optical system.This is because a decrease in F-number brings about an increase indiffraction limited frequency and the improvement of the sharpness ofthe image. Moreover, since exposure time is reduced, the image shake islessened, which is favorable. At the same time, when the surface profileof the variable mirror 409 is optimized, the sharpness of the image canbe further improved, which is more favorable. In an imaging apparatus oroptical apparatus which has no variable optical-property element, theaperture stop may, of course, be opened at the start of the electroniczoom.

FIG. 8 shows the fifth embodiment of the present invention. The opticalapparatus of the fifth embodiment has an observation optical system 900provided with the variable mirror 409 as the variable optical-propertyelement, an imaging optical system 403 provided with a variablefocal-length lens 403 d as the variable optical-property element, and anelectronic zoom function that an image recorded in the image sensor 408as a recording element by the imaging optical system 403 is magnified byimage processing. This construction is applicable to a digital camerathat has a Keplerian finder. It is also applicable to a silver-halidefilm camera. In the silver-halide film camera, the electronic zoomcannot be performed, but only a part of the film may be magnified sothat it is printed on printing paper. Alternatively, the film may beread by a film scanner so that only a necessary part of the image ismagnified and used.

The optical apparatus of the fifth embodiment is designed so that, forexample, an object (to be photographed) is observed in a wide range bythe observation optical system 900 to determine the area of the objectimage (the image to be photographed), and in accordance with thisresult, the object image is recorded in the image sensor 408 through theimaging optical system 403 and the recorded object image can bemagnified by the electronic zoom. In this optical apparatus, when theelectronic zoom is performed, the variable mirror 409 is driven throughthe driving circuit 304, including the case of focusing, so that thesharpness of the image at nearly the center of the object image formedon the image sensor 408 is heightened and the variable focal-length lens403 d placed in the imaging optical system 403 is deformed. The drivingcircuit 304 is connected to the arithmetical unit (microprocessor) 414described with reference to FIG. 1.

The observation optical system 900, as shown in FIG. 8, includes anobjective lens 902, an eyepiece 901, a prism 404, an isoscelesrectangular prism 405, a mirror 406, and the variable mirror 409.

The variable mirror 409, which includes the deformable three-layerstructure supported on the upper surface of the annular support 423, hasthe thin film 409 a in which the surface layer of the three-layerstructure constitutes a reflecting surface, the intermediate substrate409 j holding the thin film 409 a, the thin lower-layer electrode 409 k,and the plurality of electrodes 409 b arranged at preset intervals withrespect to the electrode 409 k on the lower side of the support 423. Theelectrode 409 k and the plurality of electrodes 409 b are connected to adriving circuit 304 b provided with voltage controllable, variableresistors so that preset voltages are selectively applied between theelectrode 409 k and the plurality of electrodes 409 b to deform the thinfilm 409 a. The driving circuit 304 b is connected to the arithmeticalunit (microprocessor) 414.

According to the observation optical system 900 constructed as mentionedabove, light from the object is refracted by the entrance and exitsurfaces of the objective lens 902 and the prism 404, and after beingreflected by the thin film 409 a constituting the reflecting surface ofthe variable mirror 409, passes through the prism 404. The light isfurther reflected by the isosceles rectangular prism 405 and isreflected by the mirror 406 to enter an observer's eye through theeyepiece 901. (Also, in the figure, a mark + on the optical pathindicates that a ray of light travels toward the back side of the planeof the page.)

In the observation optical system 900, when a wider area than anexpected imaging area (the area of a larger field angle than an expectedimaging field angle) is observed and then the area (the expected imagingfield angle) of an object image to be formed (an image of an object tobe photographed) is stopped down and determined, the profile of the thinfilm 409 a of the variable mirror 409 is deformed into an extendedsurface through the driving circuit 304 b by the control of thearithmetical unit 414 and a focusing adjustment is made in accordancewith an observer's diopter. At the same time, it is possible to suppressdeformations of the lenses 901 and 902 and/or the prism 404, theisosceles rectangular prism 405, and the mirror 406 and changes inrefractive index, caused by changes in temperature and humidity, or thedegradation of imaging performance by the expansion and deformation of alens frame and assembly errors of parts such as optical elements andframes. In this way, the focusing adjustment and correction foraberration produced by the focusing adjustment can be always properlymade.

On the other hand, the imaging optical system 403 includes, in orderfrom the object side, a first lens 403 a, a second lens 403 b, a stop403 c, the variable focal-length lens 403 d constructed as a third lensin which the focal length can be changed and correction for aberrationand focusing in the optical system 403 are possible, and a fourth lens403 e. Behind the imaging optical system 403, the image sensor 408 isplaced.

The imaging optical system 403 is set so that, on the basis of theinformation of the area (the expected imaging field angle) of the objectimage stopped down through the observation optical system 900, the shapeof the variable focal-length lens 403 d in the imaging optical system403 is deformed into a proper extended surface through the drivingcircuit 304 by the control of the arithmetical unit 414, and thesharpness of the image at nearly the center of the stopped-down objectimage formed on the image sensor 408 is heightened.

Thus, in the optical apparatus shown in FIG. 8, on the basis of theinformation of the area of the object image stopped down through theobservation optical system 900, the image is recorded in the imagesensor 408 by the imaging optical system 403 and the electronic zoom, asin FIG. 1, is performed with respect to the recorded image through thesignal processing circuit 308 and the image processor 303. When theimage is displayed on the display device 306, the profile of the lenssurface of the variable focal-length lens 403 d is changed so that thesharpness of the image at nearly the center of the object image (theimage of the object to be photographed) formed on the image sensor 408is heightened, or the variable focal-length lens 403 d is drived by thedriving circuit 304 so that the refractive index is changed.

According to the optical apparatus of the fifth embodiment constructedas mentioned above, in either the observation optical system or theimaging optical system of the optical apparatus, there is no need tomove a part of lens units along the optical axis for the zoom operation.Even when the electronic zoom is performed, the image is recorded in theimage sensor 408 constructed as the recording element in a state wherethe optical system is controlled so that aberration is completelyreduced. Hence, the optical apparatus can be downsized and even thoughthe zoom ratio is increased, the optical apparatus which forms an imagewith high sharpness is obtained.

In the optical apparatus of FIG. 8, unit construction in which the prism404 and the variable mirror 409 of the observation optical system 900are integrally configured is convenient for assembly. When the lenses901 and 902, the prisms 404 and 405, and the mirror 406 are molded outof plastic, curved surfaces of desired shapes can be easily configuredat will and fabrication is simple, which is favorable.

In the optical apparatus of FIG. 8, the lenses 901 and 902 are providedseparate from the prism 404, but the prisms 404 and 405, the mirror 406,and the variable mirror 409 may be designed so that aberration can beeliminated without providing the lenses 901 and 902. By doing so, theprisms 404 and 405 and the variable mirror 409 are configured into asingle optical block. This facilitates assembly.

A part or all of the lenses 901 and 902, the prisms 404 and 405, and themirror 406 may be made of glass. By doing so, the observation opticalsystem with a higher degree of accuracy is obtained. It is desirablethat the reflecting surface of the variable mirror 409 is a free-formedsurface. The free-formed surface facilitates correction for aberrationand thus is advantageous.

Each of the surfaces of the objective lens 902, the eyepiece 901, theprism 404, the isosceles rectangular prism 405, and the mirror 406 mayhave any shape such as a planar, spherical, or rotationally symmetricalaspherical surface; a planar, spherical, or rotationally symmetricalaspherical surface which has decentration with respect to the opticalaxis; an aspherical surface with symmetrical surfaces; an asphericalsurface with only one symmetrical surface; an aspherical surface with nosymmetrical surface; a free-formed surface; a surface with anondifferentiable point or line; etc., or the so-called extendedsurface.

Subsequently, reference is made to the embodiments of an optical systemapplicable to the optical apparatus of the present invention.

First Embodiment

FIG. 9 shows the first embodiment of the optical system applicable tothe optical apparatus of the present invention. FIG. 10 shows transverseaberration characteristics at the infinity of the object point distancein the first embodiment. FIG. 11 shows transverse aberrationcharacteristics at an object point distance of 150 mm in the firstembodiment. Also, arrows in FIG. 9 indicate directions of decentrationof individual optical members.

The optical system of the first embodiment, as shown in FIG. 9, includesa deformable mirror DM; a concave lens unit G1 with one lens componentcomposed of one lens element, located on the object side of thedeformable mirror DM and constructed with a negative meniscus lens witha convex surface facing the object side; an aperture stop S located onthe image side of the deformable mirror DM; a convex lens unit G2 withthree lens components composed of four lens elements, located on theimage side thereof and having a biconvex positive lens, a cementeddoublet of a biconvex positive lens and a biconcave negative lens, and abiconvex positive lens; a filter unit FL composed of a low-pass filterand an infrared cutoff filter, located behind the lens unit G2: and acover glass CG for an image sensor. A thin film constituting thereflecting surface of the deformable mirror DM is deformed and therebyfocusing is performed in the range from the infinity to a near point of150 mm. The arrangement of this optical system corresponds to that ofthe imaging optical system 301 of FIG. 1.

In the optical system of the first embodiment, when the deformablemirror DM is deformed from a planar surface into a curved surface,decentering aberration is produced by reflection from the surface of themirror. In particular, when focusing is carried out at the near pointwhere the amount of deformation of the deformable mirror DM isappreciable, the decentering aberration is increased. Thus, in order toobtain favorable optical performance in the range from the far point tothe near point, shift or tilt decentration is applied to each of thelens units or an imaging plane so that it is fixed. Whereby, theproduction of decentering aberration in focusing can be balanced. Theoptical system of the first embodiment has at least one deformablemirror DM so that focusing can be performed by only the deformation ofthe deformable mirror.

Since the optical system of the first embodiment is constructed asmentioned above, there is no need to drive lenses in focusing. As such,the optical system and the optical apparatus, which are extremely low inpower consumption, noiseless in operation, simple in mechanicalstructure, compact in design, and low in cost, can be realized.

The deformable mirror DM is controlled so that when the balance ofdecentering aberration is not maintained in focusing even by the shiftor tilt decentration applied to the lens unit or the imaging plane, thedeformable mirror is changed into a rotationally asymmetrical shape in apreset state in order to reduce the decentering aberration.

By this control, good imaging performance can be obtained in the wholefocusing region. When the deformable mirror is deformed to have power,its reflecting surface is deformed with respect to incident light andtherefore decentering aberration is produced on reflection. In order tocorrect this decentering aberration, it is desirable that the deformablemirror is changed into the rotationally asymmetrical shape in additionto the shift or tilt decentration applied to the lens unit or theimaging plane.

Also, the profile of the reflecting surface of the deformable mirror DMmay be changed so that the shift or tilt decentration is not applied tothe lens unit or the imaging plane, but decentering aberration iscorrected by the deformable mirror DM itself.

The optical system of the first embodiment is such that, in order tocorrect decentering aberration, at least one rotationally symmetricallens, the lens unit, or the imaging plane is placed so that it issubjected to the shift or tilt decentration with respect to the Z axis.

In this arrangement, as the power of the deformable mirror isstrengthened, the amount of residual decentering aberration isincreased. In such a case also, it becomes possible to obtain favorableoptical performance. Also, the decentration in the optical apparatus ofthe present invention and the optical system applied to the opticalapparatus refers to a shift or tilt.

According to the optical system of the first embodiment, the deformablemirror DM is constructed so that as the object distance for focusing isreduced, its positive power is increased. By this construction,favorable optical performance can be obtained in a wide range from thefar point to the near point. Also, in this specification, the signs ofpower are defined as plus when the mirror has a converging function andminus when it has a diverging function. That is, in the deformablemirror, as the amount of deformation of a concave surface is increased,the positive power is strengthened. The deformable mirror DM is alsoconstructed so that it is capable of having the positive power alone. Bydoing so, mechanical and electrical structures are simplified, and thedeformable mirror which is low in cost can be provided.

The deformable mirror DM may be designed to have either the positivepower or the negative power in accordance with deformation. By thisdesign, the production of decentering aberration in the deformablemirror is suppressed and good optical performance can be secured. Thatis, in the deformable mirror, the amount of deformation increases withincreasing power and thereby decentering aberration is produced to causethe deterioration of optical performance. However, the deformable mirrorhas either the positive power or the negative power to thereby controlthe amount of deformation. Thus, the production of decenteringaberration is suppressed and good optical performance can be secured.

The deformable mirror DM is constructed so that when its mirror surfaceis deformed, the periphery of the thin film constituting the mirrorsurface is fixed at the top of an annular member. The optical systemapplicable to the present invention and the optical apparatus using thisoptical system are designed to have at least one cemented lens. Thisdesign allows chromatic aberrations produced in individual lens units tobe favorably corrected and is capable of contributing to compactness ofthe optical system.

When the maximum amount of deformation of the deformable mirror isrepresented by md and the focal length of the optical system isrepresented by f, the optical system applicable to the present inventionand the optical apparatus using the optical system satisfy the followingcondition in a preset state:0<|md/f|<0.1  (3)Here, in the present invention, the focal length f of the optical systemis defined as the one where the deformable mirror has a planar shape.

By this condition, the amount of deformation of the deformable mirrorcan be kept within a proper limit. That is, beyond the upper limit ofCondition (3), the amount of deformation of the deformable mirror isextremely increased and the amount of production of decenteringaberration is increased. Consequently, it becomes difficult to fulfildesired optical performance. Moreover, the degree of difficulty offabrication becomes remarkable.

It is desirable that the optical system applicable to the presentinvention and the optical apparatus using the optical system satisfy thefollowing condition in a preset state:0<|md/f|<0.05  (3′)

By this condition, the amount of production of decentering aberrationcan be further controlled.

It is further desirable that the optical system applicable to thepresent invention and the optical apparatus using the optical systemsatisfy the following condition in a preset state:0<|md/f|<0.03  (3″)

By this condition, the amount of production of decentering aberrationcan be more favorably controlled.

When the area of an optically effective reflecting surface in thedeformable mirror is denoted by Sm, the optical system and the opticalapparatus using the optical system satisfy the following condition in apreset state:0<md ² /Sm<5.0×10⁻⁴  (4)

By this condition, the amount of deformation of the deformable mirrorcan be kept within a proper limit.

It is desirable that the optical system applicable to the presentinvention and the optical apparatus using the optical system satisfy thefollowing condition in a preset state:0<md ² /Sm<1.0×10⁻⁴  (4′)

By this condition, the amount of deformation of the deformable mirrorcan be more favorably kept within a proper limit.

The optical system including the deformable mirror applicable to thepresent invention is such that the deformable mirror is drived by anelectrostatic driving system in focusing, and when a voltage applied tothe deformable mirror in focusing is represented by Vm (volt), theoptical system satisfies the following condition in a preset state:0≦|Vm|<500  (5)

By this condition, the dangerous property of atmospheric discharge isdiminished and at the same time, the amount of deformation of thedeformable mirror can be increased.

In the optical system applicable to the present invention and theoptical apparatus using the optical system, it is desirable that whenfocusing is performed by the deformable mirror, the deformable mirror isdriven by the electrostatic driving system to satisfy the followingcondition in a preset state:0≦|Vm|<300  (5′)

By this condition, power consumption can be lowered and thus the opticalsystem and the optical apparatus that are more favorable can beprovided.

When an amount proportional to the power of the deformable mirror isdenoted by φDM, the optical system applicable to the present inventionand the optical apparatus using the optical system satisfy the followingcondition in a preset state:0≦|φDM×f|<1.00  (6)Here, the amount φDM proportional to the power of the deformable mirroris the average value of an amount φDMy proportional to the power in aplane in a decentering direction (the Y direction) of the deformablemirror and an amount φDMx proportional to the power in a plane in adirection perpendicular to the Y direction (the X direction), and isdefined as φDM=(φDMx+φDMy)/2. Also, in the present invention, C4 and C6of power components to be described later are used as φDMx=C4 andφDMy=C6.

By this condition, the focusing function of the deformable mirror can besatisfactorily performed, and decentering aberration produced in thedeformable mirror can be kept within a proper limit.

It is desirable that the optical system applicable to the presentinvention and the optical apparatus using the optical system satisfy thefollowing condition in a preset state:0≦|φDM×f|<0.50  (6′)

By this condition, decentering aberration produced in the deformablemirror can be further suppressed.

It is also desirable that the optical system applicable to the presentinvention and the optical apparatus using the optical system satisfy thefollowing condition in a preset state:0≦|φDM×f|<0.10  (6″)

By this condition, decentering aberration produced in the deformablemirror can be more favorably suppressed.

The optical system applicable to the present invention and the opticalapparatus using the optical system have the advantage that when focusingis carried out at the far point by the deformable mirror, the deformablemirror can be deformed to have lower power than in focusing. By thisconstruction, an autofocus operation of a contrast method can beperformed. Specifically, the deformable mirror has lower power than infocusing at the far point, and thereby the blurring of an image at thefar point can be adjusted.

The optical system applicable to the present invention and the opticalapparatus using the optical system have the advantage that when focusingis carried out at the near point by the deformable mirror, thedeformable mirror can be deformed to have higher power than in focusing.By this construction, the autofocus operation of the contrast method canbe performed. Specifically, the deformable mirror has higher power thanin focusing at the near point, and thereby the blurring of an image atthe near point can be adjusted.

The optical system applicable to the present invention and the opticalapparatus using the optical system are such that when focusing isperformed by the deformable mirror at the object point where the objectdistance is infinite, the deformable mirror is deformed not into aplanar surface, but into a concave surface that has larger power thanzero.

The optical system applicable to the present invention and the opticalapparatus using the optical system have a lens unit with negative poweron the object side of the deformable mirror and satisfy the followingcondition:−5.0<f1/f<−0.2  (7)where f1 is the focal length of the lens unit.

By this condition, compactness, cost reduction, and favorable opticalperformance of the deformable mirror can be obtained. That is, below thelower limit of Condition (7), the power of the lens unit with negativepower is extremely weakened, and the off-axis ray height of thedeformable mirror at the wide-angle position cannot be decreased. Thisleads to oversizing of the deformable mirror and raises cost. Beyond theupper limit of Condition (7), the power of the lens unit with negativepower is extremely strengthened, and it becomes difficult to correctcoma and chromatic aberration of magnification, produced in the lensunit.

It is desirable that the optical system applicable to the presentinvention and the optical apparatus using the optical system satisfy thefollowing condition:−2.5<f1/f<−0.5  (7′)

By this condition, favorable optical performance is ensured and at thesame time, further compactness of the deformable mirror can be achieved.

The optical system applicable to the present invention and the opticalapparatus using the optical system have the advantage that the lens unitwith negative power, located on the object side of the deformablemirror, is constructed with a single concave lens. By this construction,a compact- and slim-design optical system can be achieved because onlyone lens is placed on the object side of the deformable mirror.

When an angle at which an axial chief ray is bent by the deformablemirror is denoted by θ, the optical system applicable to the presentinvention and the optical apparatus using the optical system satisfy thefollowing condition:60°<θ<140°  (8)

Below the lower limit of Condition (8), the longitudinal dimension ofthe deformable mirror must be increased and a cost reduction becomesdifficult. Beyond the upper limit of Condition (8), the size of themirror is reduced, but lens units located in front of and behind thedeformable mirror interfere with each other, and the arrangement of theoptical system is rendered difficult. Also, the axial chief raydescribed here refers to a ray that emanates from the center of theobject, passes through the center of a stop, and reaches the center ofan image. Usually, the axial chief ray is called the optical axis.

It is desirable that the optical system applicable to the presentinvention and the optical apparatus using the optical system satisfyCondition (8′) described below. It is more desirable to satisfyCondition (8″) described below.60°<θ<120°  (8′)75°<θ<105°  (8″)

By these conditions, better results are brought about.

When the magnification of a lens unit located on the image side of thedeformable mirror, that is, a lens unit ranging from an optical surfacesituated immediately behind the deformable mirror to the last surface,is represented by β1, the optical system applicable to the presentinvention and the optical apparatus using the optical system satisfy thefollowing condition:0.2<β1<0.50  (9)

Below the lower limit of Condition (9), the magnification of the lensunit located behind the deformable mirror becomes so low that a focussensitivity of the deformable mirror is impaired and the amount ofdeformation of the deformable mirror required for focusing is increased.Beyond the upper limit of Condition (9), the magnification of the lensunit is so high that decentering aberration produced in the deformablemirror is increased and it becomes difficult to obtain satisfactoryoptical performance.

It is desirable that the optical system applicable to the presentinvention and the optical apparatus using the optical system satisfyCondition (9′) described below. It is more desirable to satisfyCondition (9″) described below.0.35<|β1|<1.50  (9′)0.50<|β1|<1.20  (9″)

By these conditions, since optical performance is ensured and the amountof deformation of the deformable mirror can be kept within a properlimit, better results are brought about.

When the overall length of the optical system is denoted by Cj, theoptical system applicable to the present invention and the opticalapparatus using the optical system satisfy the following condition:1.0<Cj/f<20.0  (10)

Beyond the upper limit of Condition (10), the overall length of theoptical system is extremely increased and compactness of the opticalsystem becomes difficult. Below the lower limit of Condition (10), thecompactness is attained, but the arrangement of lens units is limitedand satisfactory optical performance cannot be obtained.

It is desirable that the optical system applicable to the presentinvention and the optical apparatus using the optical system satisfy thefollowing condition:3.0<Cj/f<15.0  (10′)

By this condition, a compact optical system and higher opticalperformance can be obtained.

It is desirable that the optical system applicable to the presentinvention and the optical apparatus using the optical system satisfy thefollowing condition:5.0<Cj/f<10.0  (10″)

By this condition, a compact optical system and better opticalperformance can be obtained.

In order to correct decentering aberration produced by the deformablemirror, at least one lens is subjected to the shift and the opticalsystem applicable to the present invention and the optical apparatususing the optical system satisfy the following condition in a presetstate:0.0≦=|δ/f|<1.00  (11)where δ is the amount of shift of the lens.

By this condition, the amount of decentration applied to the lens can bekept within a proper limit, and the balance of optical performancebetween a weak power and a strong power of the deformable mirror can beheld. Here, the amount of shift δ refers to the amount defined as adistance between the center axis of the shifted lens and the Z axis ofthe optical system.

It is desirable that the optical system applicable to the presentinvention and the optical apparatus using the optical system satisfy thefollowing condition in a preset state:0.0≦|δ/f|<0.50  (11′)

By this condition, performance in focusing at the far and near pointscan be further improved.

It is desirable that the optical system applicable to the presentinvention and the optical apparatus using the optical system satisfy thefollowing condition in a preset state:0.0≦|δ/f|<0.25  (11″)

By this condition, the performance in focusing at the far and nearpoints can be further improved.

In order to correct decentering aberration produced by the deformablemirror, at least one lens or an imaging plane is subjected to the tiltand the optical system applicable to the present invention and theoptical apparatus using the optical system satisfy the followingcondition in a preset state:0.0°≦|ε|<10.0°  (12)where ε is the amount of tilt applied to the lens or the imaging plane.

By this condition, the amount of decentration applied to the lens can bekept within a proper limit, and the balance of optical performancebetween a weak power and a strong power of the deformable mirror can beheld. Here, the amount of tilt ε refers to the amount defined as a tiltangle made by the center axis of the tilted lens or imaging plane withthe Z axis of the optical system.

It is desirable that the optical system applicable to the presentinvention and the optical apparatus using the optical system satisfy thefollowing condition in a preset state:0.0°≦|ε|<7.0°  (12′)

By this condition, the performance in focusing at the far and nearpoints can be further improved.

It is desirable that the optical system applicable to the presentinvention and the optical apparatus using the optical system satisfy thefollowing condition in a preset state:0.0°≦|ε|<5.5°  (12″)

By this condition, the performance in focusing at the far and nearpoints can be further improved.

The optical system applicable to the present invention and the opticalapparatus using the optical system have the advantage that, of theabsolute values of the amounts of tilt applied to individual lenses orthe imaging plane, the absolute value of the amount of tilt of theimaging plane is largest.

The optical system applicable to the present invention and the opticalapparatus using the optical system have the advantage that the directionof tilt applied to the imaging plane is a direction approaching parallelto the deformable mirror.

The optical system applicable to the present invention and the opticalapparatus using the optical system have the advantage that, in theoptical system in which the shift and tilt are applied to at least onelens or an imaging plane in order to correct decentering aberrationproduced by the deformation of the deformable mirror, the shift takesplace in a certain plane and the rotary axis of the tilt isperpendicular to the plane.

The optical system applicable to the present invention and the opticalapparatus using the optical system are such that the aperture stop isplaced on the image side of the deformable mirror.

Subsequently, reference is made to the profile of the reflecting surfaceof the deformable mirror DM in the optical system applicable to thepresent invention, namely, a free-formed surface (FFS) defined by thefollowing equation. The Z axis in this defining equation corresponds tothe axis of the free-formed surface. $\begin{matrix}{Z = {{{cr}^{2}/\left\lbrack {1 + \sqrt{\left\{ {1 - {\left( {1 + k} \right)c^{2}r^{2}}} \right\}}} \right\rbrack} + {\sum\limits_{j = 2}^{N}{C_{j}X^{m}Y^{n}}}}} & (a)\end{matrix}$Here, the first term of this equation is a spherical surface term, andthe second term is a free-formed surface term. In the spherical surfaceterm, c is the curvature of the vertex, k is a conic constant,r=√{square root over ((X²+Y²))}, N is a natural number of 2 or larger, mis an integral number of 0 or larger, and n is an integral number of 0or larger.

The free-formed surface term is as follows: $\quad\begin{matrix}{{\sum\limits_{j = 2}^{N}{C_{j}X^{m}Y^{n}}} = {{C_{2}X} + {C_{3}Y} + {C_{4}X^{2}} + {C_{5}{XY}} + {C_{6}Y^{2}} +}} \\{{C_{7}X^{3}} + {C_{8}X^{2}Y} + {C_{9}{XY}^{2}} + {C_{10}Y^{3}} +} \\{{C_{11}X^{4}} + {C_{12}X^{3}Y} + {C_{13}X^{2}Y^{2}} + {C_{14}{XY}^{3}} + {C_{15}Y^{4}} +} \\{{C_{16}X^{5}} + {C_{17}X^{4}Y} + {C_{18}X^{3}Y^{2}} + {C_{19}X^{2}Y^{3}} + {C_{20}{XY}^{4}} +} \\{{C_{21}Y^{5}} + {C_{22}X^{6}} + {C_{23}X^{5}Y} + {C_{24}X^{4}Y^{2}} + {C_{25}X^{3}Y^{3}} +} \\{{C_{26}X^{2}Y^{4}} + {C_{27}{XY}^{5}} + {C_{28}Y^{6}} +} \\{{C_{29}X^{7}} + {C_{30}X^{6}Y} + {C_{31}X^{5}Y^{2}} + {C_{32}X^{4}Y^{3}} +} \\{{C_{33}X^{3}Y^{4}} + {C_{34}X^{2}Y^{5}} + {C_{35}{XY}^{6}} + {C_{36}Y^{7}\quad\ldots}}\end{matrix}$where C_(j) (j is an integral number of 2 or larger) is a coefficient.

In general, the above-mentioned free-formed surface does not have asymmetric surface for both the X-Z plane and the Y-Z plane. However, bybringing all odd-number order terms of X to 0, a free-formed surfacehaving only one symmetrical surface parallel to the Y-Z plane isobtained. By bringing all odd-number order terms of Y to 0, afree-formed surface having only one symmetrical surface parallel to theX-Z plane is obtained.

The free-formed surface of rotationally asymmetrical curved shape,mentioned above, can also be defined by the Zernike polynomial asanother defining equation. The configuration of this surface is definedby the following equation. The Z axis of this equation corresponds tothe axis of the Zernike polynomial. The rotationally asymmetricalsurface is defined by polar coordinates of a height from the Z axisrelative to the X-Y plane, where R is a distance from the Z axis in theX-Y plane, and A is an azimuth around the Z axis and is expressed by anrotating angle measured from the Z axis. $\begin{matrix}{{X = {R \times {\cos(A)}}}Y = {R \times {\sin(A)}}} & (b) \\\begin{matrix}{Z = {D_{2} + {D_{3}R\quad{\cos(A)}} + {D_{4}R\quad{\sin(A)}} + {D_{5}R^{2}{\cos\left( {2\quad A} \right)}} + {D_{6}\left( {R^{2} - 1} \right)} +}} \\{{D_{7}R^{2}{\sin\left( {2\quad A} \right)}} + {D_{8}R^{3}\cos\quad\left( {3\quad A} \right)} + {{D_{9}\left( {{3\quad R^{3}} - {2\quad R}} \right)}{\cos(A)}} +} \\{{{D_{10}\left( {{3\quad R^{3}} - {2\quad R}} \right)}{\sin(A)}} + {D_{11}R^{3}{\sin\left( {3\quad A} \right)}} + {D_{12}R^{4}{\cos\left( {4\quad A} \right)}} +} \\{{{D_{13}\left( {{4\quad R^{4}} - {3\quad R^{2}}} \right)}{\cos\left( {2\quad A} \right)}} + {D_{14}\left( {{6\quad R^{4}} - {6\quad R^{2}} + 1} \right)} +} \\{{{D_{15}\left( {{4\quad R^{4}} - {3\quad R^{2}}} \right)}{\sin\left( {2A} \right)}} + {D_{16}R^{4}{\sin\left( {4\quad A} \right)}} + {D_{17}R^{5}{\cos\left( {5\quad A} \right)}} +} \\{{{D_{18}\left( {{5\quad R^{5}} - {4\quad R^{3}}} \right)}{\cos\left( {3\quad A} \right)}} + {{D_{19}\left( {{10\quad R^{5}} - {12\quad R^{3}} + {3\quad R}} \right)}{\cos(A)}} +} \\{{{D_{20}\left( {{10\quad R^{5}} - {12\quad R^{3}} + {3\quad R}} \right)}{\sin(A)}} + {{D_{21}\left( {{5\quad R^{5}} - {4\quad R^{3}}} \right)}{\sin\left( {3\quad A} \right)}} +} \\{{D_{22}R^{5}{\sin\left( {5\quad A} \right)}} + {D_{23}R^{6}{\cos\left( {6\quad A} \right)}} + {{D_{24}\left( {{6\quad R^{6}} - {5\quad R^{4}}} \right)}{\cos\left( {4\quad A} \right)}} +} \\{{{D_{25}\left( {{15\quad R^{6}} - {20\quad R^{4}} + {6\quad R^{2}}} \right)}{\cos\left( {2\quad A} \right)}} +} \\{{D_{26}\left( {{20\quad R^{6}} - {30\quad R^{4}} + {12\quad R^{2}} - 1} \right)} +} \\{{{D_{27}\left( {{15\quad R^{6}} - {20R^{4}} + {6\quad R^{2}}} \right)}{\sin\left( {2\quad A} \right)}} +} \\{{{D_{28}\left( {{6\quad R^{6}} - {5\quad R^{4}}} \right)}{\sin\left( {4\quad A} \right)}} + {D_{29}R^{6}{\sin\left( {6\quad A} \right)}\quad\ldots}}\end{matrix} & \quad\end{matrix}$where D_(m) (m is an integral number of 2 or larger) is a coefficient.Also, in order to make a design as an optical system symmetrical withrespect to the X axis, D₄, D₅, D₆, D₁₀, D₁₁, D₁₂, D₁₃, D₁₄, D₂₀, D₂₁,D₂₂, . . . are used.

The above defining equation is shown to give an example of theconfiguration of the rotational asymmetrical curved surface, and it isneedless to say that the same effect is secured with respect to anyother defining equation. If mathematically identical values are given,the configuration of the curved surface may be expressed by anotherdefinition.

In the present invention, all odd-number order terms of X in Equation(a) are brought to zero and thereby the free-formed surface that has asymmetrical surface parallel to the Y-Z plane is obtained.

Also, when Z is taken as the coordinate in the direction of the opticalaxis, Y is taken as the coordinate normal to the optical axis, krepresents a conic constant, and a, b, c, and d represent asphericalcoefficients, the configuration of an aspherical surface is expressed bythe following equation:Z=(Y ² /r)/[1+{1−(1+k)·(Y/r)²}^(1/2) ]+ay ⁴ +by ⁶ +cy ⁸ +dy ¹⁰  (c)

These symbols are also used for the numerical data of the embodiments tobe described later.

In the embodiments, “ASP” denotes an aspherical surface, “FFS” denotes afree-formed surface, and “DM” denotes a deformable mirror. The termsrelative to the aspherical surface and the free-formed surface that arenot set forth in the data are zero. The refractive index and the Abbe'snumber are described with respect to the d line (wavelength 587.56 nm).The length is expressed in millimeters (mm) and the angle in degrees(deg). Also, although two or three plane-parallel plates are arranged onthe most image-plane side in each of the embodiments, they are assumedas the cover glass of an image sensor, a low-pass filter placed ahead ofthe cover glass, and an IR cutoff filter ahead thereof. Also, when thelow-pass filter coated with the IR cutoff filter is fabricated, twoplane-parallel plates are obtained.

In each embodiment, the Z axis of the coordinate system on the surfaceof an object is defined as a straight line perpendicular to the surfaceof the object, passing through the center of the object. The Y axis istaken as the coordinate normal to the Z axis, and the X axis is taken asan axis constituting a right-handed coordinate system together with theY axis and the Z axis. The optical axis is defined as the path of a rayof light passing through the centers of the surface of the object andthe stop or the exit pupil. Thus, the optical axis is changed with thedeformation of the deformable mirror, but this change is slight in mostcases. Consequently, the Z axis practically coincides with the opticalaxis in each embodiment.

A decentering surface is given by the shift of the vertex position ofthis surface (the directions of X, Y, and Z axes are denoted by X, Y,and Z, respectively) from the origin of the coordinate system and by thetilt (α, β, and γ (deg)) of the center axis of the surface (the Z axisof Equation (a) in the free-formed surface), with the X, Y, and Z axesas centers. When a surface to be decentered is called a k surface, theorigin of the coordinate system where decentration takes place isdefined as a point shifted from the vertex position of a k−1 surfacealong the Z axis for surface-to-surface spacing. The decentration takesplace in order of X shift, Y shift, Z shift, α tilt, β tilt, and γ tilt.In this case, the plus sign of each of α and β indicates acounterclockwise direction where each of the X axis and the Y axis isviewed from a minus side, and the plus sign of γ indicates a clockwisedirection where the Z axis is viewed from a minus direction.

Also, in each embodiment, there are two kinds of decentration,decenter-and-return (DAR) and decenter-only (DEO). In the DAR, when thek surface has been decentered, each of the coordinate systems of a k+1surface and surfaces lying behind it coincides with that of the ksurface before decentration. The vertex position of the k+1 surface isdefined as a point shifted from that of the k surface beforedecentration along the Z axis for surface-to-surface spacing. In theDEO, on the other hand, when the k surface has been decentered, each ofthe coordinate systems of the k+1 surface and surfaces lying behind itcoincides with that of the k surface after decentration. The vertexposition of the k+1 surface is defined as a point shifted from that ofthe k surface after decentration along the Z axis for surface-to-surfacespacing.

The positive direction of the Z axis of the coordinate system of areflecting surface refers to a direction in which the axis travels fromthe obverse of the reflecting surface toward the reverse. Thus, when thereflecting surface is changed into the free-formed surface shapeexpressed by the X-Y polynomial and the power components C₄ and C₆ arepositive, the reflecting surface becomes a convex mirror, that is, amirror with negative power. Conversely, when the power components C₄ andC₆ are negative, a concave mirror, that is, a mirror with positivepower, is obtained. The coordinate system of the optical system after alight ray is reflected by the reflecting surface corresponds to the casewhere the coordinate system before the ray is reflected is rotated by180° about the X axis. Whereby, the ray always travels along thepositive direction of the Z axis of the optical system.

The deformable mirror is capable of changing the power to performfocusing from the far point to the near point, but is designed to bringabout a state of weaker power than in focusing at the far point and astate of stronger power than in focusing at the near point in order toperform auto-focusing of a contrast method. In each embodiment to bedescribed below, the state of weaker power than in focusing at the farpoint is defined as far-point allowance, and a state of stronger powerthan in focusing at the near point is defined as near-point allowance.That is, the deformable mirror has four states, the far-point allowance,the far point, the near point, and the near-point allowance.

The deformable mirror in each embodiment is designed to have anallowance for the amount of deformation before and after the focusingrange, in view of the shift of the image plane in the Z direction causedby a fabrication error in actual fabrication and by a temperaturechange.

As mentioned above, since the focusing function is imparted to thedeformable mirror and thereby focusing can be performed withoutmechanical drive, a lens frame structure is simplified and a compactdesign and a cost reduction can be attained. Moreover, there is themerit of eliminating the driving noise of a motor in focusing.

FIGS. 12-15 are graphs, each showing a wave optical MTF (140 lines/mm)at 9.67° in the −Y direction of the object (which refers to theorientation of the object where X is 0.000° and Y is −9.67°) whentwofold electronic zoom is performed by the optical system of the firstembodiment. Specifically, the size of the imaging surface of the imagesensor is thought of as 2 mm×1.5 mm, and graphs showing the MTF wherethe shape of the thin film 409 a is optimized so that the sharpness ofthe image is improved in the area of the imaging surface are given inFIG. 12 (object distance ∞) and FIG. 13 (object distance 150 mm). Also,the pixel size of the image sensor is 2.5 microns and the number ofpixels is two million. The electronic zoom magnification β_(E)=2satisfies Conditions (1) and (1′). For comparison, graphs of the MTFwhere the shape of the thin film 409 a is not optimized are shown inFIG. 14 (object distance ∞) and FIG. 15 (object distance 150 mm). Thatis, these are the same as the MTF at the center of image where theelectronic zoom is not performed.

Comparison of FIGS. 12 and 13 with FIGS. 14 and 15 shows that the MTF ina state where the size of the imaging surface is limited to 2 mm×1.5 mmand the shape of the thin film 409 a is optimized is improved incontrast with that in a state where the shape is not optimized, namely,the size of the imaging surface is 4 mm×3 mm.

Subsequently, numerical data of optical members constituting the opticalsystem of the first embodiment are shown below. Numerical data 1 Focallength: 4.4 mm (38 mm in terms of silver halide) Open F-number: 2.8 Sizeof imaging surface: 4.0 mm × 3.0 mm (X direction × Y direction) Surfacenumber Radius of curvature Surface spacing Decentration Refractive indexAbbe's number Object surface ∞ ∞  1 ASP [1] 0.800 Decentration 1.814132.2 (1)  2 ASP [2] 4.200 Decentration (1)  3 ∞ 0.000 Decentration (2) 4 FFS [1] 0.000 Decentration (3)  5 ∞ 3.800 Decentration (4)  6 (stop ∞0.100 surface)  7 ASP [3] 2.000 Decentration 1.7465 51.1 (5)  8 ASP [4]5.438 Decentration (5)  9 7.324 2.021 Decentration 1.5011 68.3 (6) 10−7.973 0.800 Decentration 1.8307 24.5 (6) 11 5.885 0.300 Decentration(6) 12 5.787 2.000 Decentration 1.4900 70.0 (7) 13 ASP [5] 1.626Decentration (7) 14 ∞ 1.000 1.5163 64.1 15 ∞ 1.290 1.5477 62.8 16 ∞0.800 17 ∞ 0.750 1.5163 64.1 18 ∞ 1.200 Image plane ∞ 0.000 Decentration(8) Aspherical coefficients ASP [1] Radius of curvature 70.428 k = 0 a =2.2133 × 10⁻³ b = −4.1162 × 10⁻⁴ c = 2.4537 × 10⁻⁵ d = −3.6373 × 10⁻⁷ASP [2] Radius of curvature 3.507 k = 0 a = 2.1789 × 10⁻³ b = −4.6380 ×10⁻⁴ c = −3.9638 × 10⁻⁵ d = 5.3918 × 10⁻⁶ ASP [3] Radius of curvature13.911 k = 0 a = 5.4052 × 10⁻⁵ b = −2.3064 × 10⁻⁶ c = 1.0798 × 10⁻⁶ d =3.3961 × 10⁻⁸ ASP [4] Radius of curvature −9.140 k = 0 a = 3.7861 × 10⁻⁴b = 6.5188 × 10⁻⁶ c = −8.0902 × 10⁻⁸ d = 9.8151 × 10⁻⁸ ASP [5] Radius ofcurvature −8.610 k = 0 a = 1.3105 × 10⁻³ b = −2.6285 × 10⁻⁵ c = 2.0896 ×10⁻⁶ d = −9.3284 × 10⁻⁸ Amount of decentration Decentration [1] (DAR) X= 0.000 Y = −0.455 Z = 0.000 α = 0.000 β = 0.000 γ = 0.000 Decentration[2] (DEO) X = 0.000 Y = 0.000 Z = 0.000 α = 45.000 β = 0.000 γ = 0.000Decentration [3] (DAR) X = 0.000 Y (described in FFS [1]) Z (describedin FFS [1]) α = −0.783 β = 0.000 γ = 0.000 Decentration [4] (DEO) X =0.000 Y = 0.000 Z = 0.000 α = 45.000 β = 0.000 γ = 0.000 Decentration[5] (DAR) X = 0.000 Y = 0.428 Z = 0.000 α = 0.000 β = 0.000 γ = 0.000Decentration [6] (DAR) X = 0.000 Y = 0.270 Z = 0.000 α = 0.000 β = 0.000γ = 0.000 Decentration [7] (DAR) X = 0.000 Y = 0.147 Z = 0.000 α = 0.000β = 0.000 γ = 0.000 Decentration [8] (DAR) X = 0.000 Y = 0.000 Z = 0.000α = −2.000 β = 0.000 γ = 0.000 FFS [1] State 1: Far-point allowance (∞)C4 = 0.00000 C6 = 0.00000 C8 = 0.00000 C10 = 0.00000 C11 = 0.00000 C13 =0.00000 C15 = 0.00000 X = 0 Y = 0 Z = 0 State 2: Far point (∞) C4 =−0.5892 × 10⁻³ C6 = −0.3128 × 10⁻³ C8 = −0.3938 × 10⁻⁴ C10 = −0.2812 ×10⁻⁴ C11 = 0.2639 × 10⁻⁵ C13 = −0.2463 × 10⁻⁵ C15 = −0.2641 × 10⁻⁵ X = 0Y = 0.47001 Z = 0.00338 State 3: Near point (150 mm) C4 = −0.1086 × 10⁻²C6 = −0.6189 × 10⁻³ C8 = −0.6338 × 10⁻⁴ C10 = −0.4815 × 10⁻⁴ C11 =0.3921 × 10⁻⁵ C13 = 0.6584 × 10⁻⁶ C15 = −0.2915 × 10⁻⁵ X = 0 Y = 0.34044Z = 0.00643 State 4: Near-point allowance (150 mm) C4 = −0.1575 × 10⁻²C6 = −0.9311 × 10⁻³ C8 = −0.9810 × 10⁻⁴ C10 = −0.7349 × 10⁻⁴ C11 =0.5562 × 10⁻⁶ C13 = −0.2496 × 10⁻⁵ C15 = −0.4413 × 10⁻⁵ X = 0 Y =0.36255 Z = 0.00964 State 5: Far point (∞) where the variable mirror isoptimized in accordance with twofold electronic zoom. FFS [1] C4 =−6.3929474 × 10⁻⁴ C6 = −3.6980265 × 10⁻⁴ C8 = −2.8038856 × 10⁻⁵ C10 =−1.8430997 × 10⁻⁵ C11 = 1.1082276 × 10⁻⁶ C13 = −3.6490148 × 10⁻⁷ C15 =−7.0733077 × 10⁻⁷ X = 0 Y = 1.6130766 Z = 1.5976326 × 10⁻² Decentration[3] (DAR) X(described in FFS [1]) Y (described in FFS [1]) Z (describedin FFS [1]) α = −8.4693588 × 10⁻¹ β = 0.000 γ = 0.000 md = 0.003 In thisstate, the value of md is different from that of the decentration Z.Data of other surfaces are the same as in States 1-4. State 6:Near-point (150 mm) where the variable mirror is optimized in accordancewith twofold electronic zoom. FFS [1] C4 = −8.6605429 × 10⁻⁴ C6 =−3.3179512 × 10⁻⁴⁷ C8 = −8.2667455 × 10⁻⁵ C10 = −3.1749661 × 10⁻⁵ C11 =7.4217471 × 10⁻⁶ C13 = −1.6164728 × 10⁻⁷ C15 = −2.8477659 × 10⁻⁶ X = 0 Y= −1.7740545 Z = −9.0076818 × 10⁻³ Decentration [3] (DAR) X(described inFFS [1]) Y (described in FFS [1]) Z (described in FFS [1]) α =−8.4693588 × 10⁻¹ β = 0.000 γ = 0.000 md = 0.006

In this state, the value of md is different from that of thedecentration Z.

Data of other surfaces are the same as in States 1-4.

Subsequently, values of parameters of individual conditions in the firstembodiment are shown in Tables 1A and 1B. TABLE 1A Condition State 1State 2 State 3 State 4 Object distance ∞ allowance ∞ 150 mm 150 mmallowance φDMx (power x) 0.000 × 10⁰ −5.892 × 10⁻⁴ −1.086 × 10⁻³ −1.575× 10⁻³ [1/mm] φDMy (power y) 0.000 × 10⁰ −3.128 × 10⁻⁴ −6.189 × 10⁻⁴−9.311 × 10⁻⁴ [1/mm] md (the amount of 0.000 × 10⁰  3.380 × 10⁻³  6.430× 10⁻³  9.640 × 10⁻³ deformation) [mm] β 1 (magnification of (9) −0.995−0.995 −0.994 −0.993 rear lens unit) f (focal length) 4.538 4.538 4.5384.538 [mm] Cj (overall length of 28.250 28.250 28.250 28.250 opticalsystem) [mm] Sm (mirror area) 25.525 25.525 25.525 25.525 [mm²] f 1(focal length of −4.558 −4.558 −4.558 −4.558 front lens unit) [mm] δ(maximum value of 0.455 0.455 0.455 0.455 shift) [mm] ε (maximum valueof (12) −2.000 −2.000 −2.000 −2.000 tilt) [deg] |md/f| (3) 0.000 × 10⁰7.448 × 10⁻⁴ 1.417 × 10⁻³ 2.124 × 10⁻³ md²/Sm (4) 0.000 × 10⁰ 4.476 ×10⁻⁷ 1.620 × 10⁻⁶ 3.641 × 10⁻⁶ |φDM × f| (6) 0.000 × 10⁰ 2.047 × 10⁻⁴3.868 × 10⁻³ 5.686 × 10⁻³ f1/f (7) −1.004 −1.004 −1.004 −1.004 Cj/f (10)6.225 6.225 6.225 6.225 |δ/f| (11) 0.100 0.100 0.100 0.100

TABLE 1B Condition State 5 State 6 Object distance ∞ 150 mm φDMx (powerx) −6.393 × 10⁻⁴ −8.661 × 10⁻⁴ [l/mm] φDMy (power y) −3.698 × 10⁻⁴−3.318 × 10⁻⁴ [l/mm] md (the amount of    3 × 10⁻³    6 × 10⁻³deformation) [mm] β1 (magnification of (9) −0.995 −0.994 rear lens unit)f (focal length) 4.538 4.538 [mm] Cj (overall length of 28.250 28.250optical system) [mm] Sm (mirror area) 25.525 25.525 [mm²] f1 (focallength of −4.558 −4.558 front lens unit) [mm] δ (maximum value of 0.4550.455 shift) [mm] ε (maximum value of (12) −2.000 −2.000 tilt) [deg]|md/f| (3)   6.6 × 10⁻⁴  1.32 × 10⁻³ md²/Sm (4)  3.52 × 10⁻⁷  1.41 ×10⁻⁶ |φDM × f| (6)  2.290 × 10⁻³  2.718 × 10⁻³ f1/f (7) −1.004 −1.004Cj/f (10) 6.225 6.225 |δ/f| (11) 0.100 0.100

Second Embodiment

FIGS. 16, 17, and 18 show the second embodiment of the optical systemapplicable to the optical apparatus of the present invention, atwide-angle, middle, and telephoto positions, respectively.

The deformable mirror of the second embodiment is capable of changingthe power to perform focusing in the range from the far point to thenear point, but is designed to bring about a state of weaker power thanin focusing at the far point and a state of stronger power than infocusing at the near point in order to perform the autofocus operationof a contrast method. In the second embodiment, the state of weakerpower than in focusing at the far point is defined as far-pointallowance, and a state of stronger power than in focusing at the nearpoint is defined as near-point allowance. That is, the deformable mirrorhas four states, the far-point allowance, the far point, the near point,and the near-point allowance, and in addition to each of these states,three states, the wide-angle, middle, and telephoto positions. Thus, intotal, 12 states are brought about.

The deformable mirror in the second embodiment is designed to have anallowance for the amount of deformation before and after the focusingrange, in view of the shift of the image plane in the Z direction causedby a fabrication error in actual fabrication and by a temperaturechange.

The optical system of the second embodiment includes, in order from theobject side, a fixed lens unit G1′ with negative power, the deformablemirror DM, a fixed lens unit 15′ with positive power, a moving lens unitG2′ with positive power, the stop S, a fixed lens unit G3′ with negativepower, a moving lens unit G4′ with positive power, and a fixed lens unitG5′ with positive power. In FIGS. 16-18, again, reference symbol FLdesignates the filter unit.

The fixed lens unit G1′ is constructed with a biconcave negative lens.The fixed lens unit G15′ has a positive meniscus lens with a convexsurface facing the object side. The moving lens unit G2′ is constructedwith a cemented doublet of a negative meniscus lens with a convexsurface facing the object side and a biconvex positive lens. The fixedlens unit G3′ is constructed with a cemented doublet of a biconcavenegative lens and a positive meniscus lens with a convex surface facingthe object side. The moving lens unit G4′ has a biconvex positive lensand a cemented doublet of a biconvex positive lens and a biconcavenegative lens. The fixed lens unit G5′ is constructed with a biconvexpositive lens.

The optical system of the second embodiment is provided with a variablemagnification function by moving the moving lens units G2′ and G4′. Thethin film constituting the reflecting surface of the deformable mirrorDM is deformed, and thereby focusing can be carried out in the rangefrom the infinity to a near point of 300 mm.

When the thin film of the deformable mirror is deformed from a planarsurface into a curved surface, decentering aberration is produced byreflection from a mirror surface. In particular, when focusing iscarried out at the nearest point where the amount of deformation of thedeformable mirror DM is appreciable, the decentering aberration isincreased. Thus, in the second embodiment; to obtain favorable opticalperformance in the range from the far point to the near point, shift ortilt decentration is applied to a lens unit or an imaging plane.Whereby, the production of decentering aberration in focusing isbalanced.

According to the optical system in the first and second embodiments,since focusing can be performed without mechanical drive, a lens framestructure is simplified and a compact design and a cost reduction can beattained. Moreover, there is the merit of eliminating the driving noiseof a motor in focusing.

Also, although in the first embodiment the variable mirror is placed inthe optical system and thereby various functions and effects are broughtabout, identical functions and effects can be obtained in the secondembodiment.

Subsequently, numerical data optical members constituting the opticalsystem of the second embodiment are shown below. Numerical data 2 Focallength: 4.4 mm (wide-angle) ˜13.2 mm (telephoto), 7.6 mm (middle) OpenF-number: 2.4˜5.3 Size of imaging surface: 4.0 mm × 3.0 mm (X direction× Y direction) Lens-to-lens spacing is changed in order of(wide-angle)-(middle)-(telephoto) Surface number Radius of curvatureSurface spacing Decentration Refractive index Abbe's number Objectsurface ∞ ∞  1 (virtual plane) ∞ 0.00  2 −50.75 1.00 Decentration (1)1.7800 50.0  3 ASP [1] 0.00  4 (virtual plane) ∞ 6.60  5 (virtual plane)∞ 0.00  6 (virtual plane) ∞ 0.00  7 (virtual plane) ∞ 0.00 Decentration(2)  8 FFS [1] 0.00 Decentration (3)  9 (virtual plane) ∞ 0.00Decentration (2) 10 (virtual plane) ∞ 4.64 11 19.94 1.27 Decentration(4) 1.8500 24.0 12 29.66 0.10 Decentration (4) 13 (virtual plane) ∞8.44˜1.70˜0.00 14 21.47 1.00 Decentration (5) 1.8500 24.0 15 10.21 1.86Decentration (5) 1.6173 57.3 16 ASP[2] 1.70˜8.44˜10.14 Decentration (5)17 (stop surface) 1.00 Decentration (6) 1.7281 48.3 18 11.26 1.33Decentration (6) 1.8500 24.0 19 77.41 0.10 Decentration (6) 20 (virtualplane) ∞ 8.45˜6.07˜0.10 21 ASP [3] 3.56 Decentration (7) 1.4900 70.0 22ASP [4] 0.75 Decentration (7) 23 9.80 2.77 Decentration (8) 1.5269 65.124 −7.45 3.89 Decentration (8) 1.7727 31.5 25 4.26 3.27˜5.65˜11.62Decentration (8) 26 (virtual plane) ∞ 0.00 27 7.43 2.13 Decentration (9)1.4900 70.0 28 −14.27 0.30 Decentration (9) 29 ∞ 1.44 1.5477 62.8 30 ∞0.10 31 ∞ 0.60 1.5163 64.1 32 ∞ 0.50 33 (virtual plane) ∞ 0.00 Imageplane ∞ 0.00 Decentration (10) Aspherical coefficients ASP [1] Radius ofcurvature 7.18 k = 0 a = −3.8858 × 10⁻⁴ b = −3.6372 × 10⁻⁶ c = −8.8491 ×10⁻⁸ d = 3.2705 × 10⁻¹⁰ ASP [2] Radius of curvature −16.03 k = 0 a =4.4224 × 10⁻⁵ b = 5.4185 × 10⁻⁹ c = 1.6428 × 10⁻⁸ d = −7.0199 × 10⁻¹⁰ASP [3] Radius of curvature 7.70 k = 0 a = −1.6991 × 10⁻⁴ b = −1.7112 ×10⁻⁷ c = 3.8286 × 10⁻⁸ d = −7.0832 × 10⁻⁹ ASP [4] Radius of curvature−12.01 k = 0 a = 2.8459 × 10⁻⁴ b = 1.9921 × 10⁻⁶ c = −1.3381 × 10⁻⁷ d =−3.1611 × 10⁻⁹ Amount of decentration Decentration [1] (DEO) X = 0.00 Y= 0.06 Z = 0.00 α = −0.76 β = 0.00 γ = 0.00 Decentration [2] (DAR) X =0.00 Y = 0.00 Z = 0.00 α = 45.00 β = 0.00 γ = 0.00 Decentration [3](DAR) X = 0.00 Y (described in FFS [1]) Z (described in FFS [1]) α =−0.29 β = 0.00 γ = 0.00 Decentration [4] (DAR) X = 0.00 Y = 0.00 Z =0.00 α = 0.00 β = 0.00 γ = 0.00 Decentration [5] (DAR) X = 0.00 Y =−0.05 Z = 0.00 α = 0.00 β = 0.00 γ = 0.00 Decentration [6] (DAR) X =0.00 Y = 0.07 Z = 0.00 α = 0.00 β = 0.00 γ = 0.00 Decentration [7] (DAR)X = 0.00 Y = −0.01 Z = 0.00 α = 0.00 β = 0.00 γ = 0.00 Decentration [8](DAR) X = 0.00 Y = 0.00 Z = 0.00 α = 0.00 β = 0.00 γ = 0.00 Decentration[9] (DAR) X = 0.00 Y = 0.19 Z = 0.00 α = 0.00 β = 0.00 γ = 0.00Decentration [10] (DAR) X = 0.00 Y = 0.00 Z = 0.00 α = 1.15 β = 0.00 γ =0.00

However, the coordinate system of the fourth surface is the same as thatof the first surface. The coordinate systems after the fifth surface aredefined in order from the fourth surface. FFS [1] State 1: Wide-angle,far-point allowance (∞) State 2: Middle, far-point allowance (∞) State3: Telephoto, Far-point allowance (∞) In these three states, all ofC4-C21 are zero. All values of Y and Z in the decentration are alsozero. State 4: Wide-angle, far-point (∞) C4 = −5.8995 × 10⁻⁴ C6 =−2.9424 × 10⁻⁴ C8 = −1.1899 × 10⁻⁵ C10 = −5.2364 × 10⁻⁶ C11 = 6.5392 ×10⁻⁶ C13 = 5.6143 × 10⁻⁶ C15 = 1.5847 × 10⁻⁶ C17 = 5.4357 × 10⁻⁷ C19 =−1.9838 × 10⁻⁸ C21 = 1.4414 × 10⁻⁷ X = 0 Y = 2.5683618 × 10⁻² Z =7.5651900 × 10⁻³ State 5: Middle, far-point C4 = −2.2653 × 10⁻⁴ C6 =−1.1179 × 10⁻⁴ C8 = −7.6259 × 10⁻⁶ C10 = −2.9580 × 10⁻⁶ C11 = 2.5261 ×10⁻⁶ C13 = 1.9724 × 10⁻⁶ C15 = 6.5262 × 10⁻⁷ C17 = 2.5658 × 10⁻⁷ C19 =−7.4094 × 10⁻⁸ C21 = 5.0196 × 10⁻⁸ X = 0 Y = 6.7269098 × 10⁻² Z =2.7958048 × 10⁻³ State 6: Telephoto, far-point (∞) C4 = −1.0629 × 10⁻⁴C6 = −5.1178 × 10⁻⁵ C8 = −3.0545 × 10⁻⁶ C10 = −1.3201 × 10⁻⁶ C11 =1.7419 × 10⁻⁶ C13 = 1.5053 × 10⁻⁶ C15 = 3.9446 × 10⁻⁷ C17 = 1.1609 ×10⁻⁷ C19 = −7.8183 × 10⁻⁸ C21 = 2.1350 × 10⁻⁸ X = 0 Y = −2.8997388 ×10⁻¹ Z = 1.1937900 × 10⁻³ State 7: Wide-angle, near-point (300 mm) C4 =−8.9987 × 10⁻⁴ C6 = −4.6031 × 10⁻⁴ C8 = −1.2709 × 10⁻⁵ C10 = −9.2227 ×10⁻⁶ C11 = 5.8328 × 10⁻⁶ C13 = 5.2240 × 10⁻⁶ C15 = 1.3529 × 10⁻⁶ C17 =−1.3885 × 10⁻⁷ C19 = 2.9544 × 10⁻⁷ C21 = 1.2636 × 10⁻⁷ X = 0 Y =1.8131829 × 10⁻¹ Z = 1.2704720 × 10⁻² State 8: Middle, near-point (300mm) C4 = −5.5202 × 10⁻⁴ C6 = −2.8215 × 10⁻⁴ C8 = −1.5110 × 10⁻⁵ C10 =−8.0880 × 10⁻⁶ C11 = 1.0816 × 10⁻⁶ C13 = 8.5525 × 10⁻⁷ C15 = −2.4178 ×10⁻⁷ C17 = −2.6235 × 10⁻⁷ C19 = −1.2175 × 10⁻⁸ C21 = −6.1369 × 10⁻⁸ X =0 Y = 4.6081175 × 10⁻¹ Z = 8.3554983 × 10⁻³ State 9: Telephoto,near-point (300 mm) C4 = −4.4543 × 10⁻⁴ C6 = −2.3298 × 10⁻⁴ C8 = −1.5323× 10⁻⁵ C10 = −9.3389 × 10⁻⁶ C11 = 6.7912 × 10⁻⁷ C13 = 3.7985 × 10⁻⁷ C15= 5.8882 × 10⁻⁸ C17 = −1.2604 × 10⁻⁷ C19 = 9.7671 × 10⁻⁸ C21 = 4.6322 ×10⁻⁸ X = 0 Y = 4.5036089 × 10⁻¹ Z = 6.7530421 × 10⁻³ State 10:Wide-angle, near-point allowance (300 mm) C4 = −1.4304 × 10⁻³ C6 =−7.4243 × 10⁻⁴ C8 = −3.0911 × 10⁻⁵ C10 = −2.5613 × 10⁻⁵ C11 = 7.5650 ×10⁻⁶ C13 = 5.8627 × 10⁻⁶ C15 = 2.0048 × 10⁻⁶ C17 = −2.3602 × 10⁻⁷ C19 =1.0980 × 10⁻⁶ C21 = 4.6601 × 10⁻⁷ X = 0 Y = 2.6318036 × 10⁻¹ Z =2.0749379 × 10⁻² State 11: Middle, near-point allowance (300 mm) C4 =−7.6639 × 10⁻⁴ C6 = −3.9897 × 10⁻⁴ C8 = −2.6746 × 10⁻⁵ C10 = −1.4551 ×10⁻⁵ C11 = 2.3683 × 10⁻⁶ C13 = 2.2765 × 10⁻⁶ C15 = 2.1997 × 10⁻⁷ C17 =1.3439 × 10⁻⁷ C19 = 4.1759 × 10⁻⁷ C21 = 5.7639 × 10⁻⁸ X = 0 Y =4.6261205 × 10⁻¹ Z = 1.1455965 × 10⁻² State 12: Telephoto, near-pointallowance (300 mm) C4 = −5.4800 × 10⁻⁴ C6 = −2.8654 × 10⁻⁴ C8 = −2.1514× 10⁻⁵ C10 = −1.1640 × 10⁻⁵ C11 = 1.1846 × 10⁻⁶ C13 = 1.8790 × 10⁻⁷ C15= 1.4185 × 10⁻⁷ C17 = 1.0460 × 10⁻⁷ C19 = 1.0214 × 10⁻⁷ C21 = 7.2358 ×10⁻⁸ X = 0 Y = 4.5428613 × 10⁻¹ Z = 8.2647224 × 10⁻³

FIG. 19 is a graph showing the wave optical MTF (140 lines/mm) wheretwofold electronic zoom is performed in the optical system of the secondembodiment of FIGS. 16-18. The optical system is in the telephoto stateand has an object point distance of ∞. In five object positionsindicated at the bottom of FIG. 19, the graphs of the MTF aresuperimposed.

FIG. 20 is a graph showing the MTF where the shape of the variablemirror is optimized with respect to only a part of the image used whenthe electronic zoom is performed in the optical system of the secondembodiment of FIGS. 16-18. The calculating condition of the MTF is thesame as in FIG. 19. Comparison with FIG. 19 shows that the MTF of FIG.20 is improved.

Subsequently, numerical data of optical members constituting the opticalsystem of the second embodiment in a state of FIG. 20 are shown below.Only the data of the eighth surface are shown here. The numerical dataof other surfaces are the same as in State 6 of the numerical data inthe second embodiment.

State 13: When the variable mirror is optimized in accordance with theelectronic zoom, FFS [1] C4 = −2.7203 × 10⁻⁴ C6 = −1.3596 × 10⁻⁴ C8 =−4.0935 × 10⁻⁶ C10 = −1.9999 × 10⁻⁶ C11 = 1.5109 × 10⁻⁶ C13 = 1.6613 ×10⁻⁶ C15 = 4.9016 × 10⁻⁷ C17 = 1.2327 × 10⁻⁷ C19 = 1.3220 × 10⁻⁷ C21 =3.9806 × 10⁻⁸ Decentration [3] X = 0.00 Y = 2.6902975 × 10⁻² Z =3.7656323 × 10⁻³ α = −2.5095701 × 10⁻¹ β = 0.00 γ = 0.00

Also, Conditions (1′), (2), (3), (3′), (3″), (4), (4′), (5), (5′), (6),(6′), (6″), (7), (7′), (8), (8′), (9), (9′), (10), (10′), (10″), (11),(11′), (11″), (12), (12′), and (12″), like the optical system of thefirst embodiment, also hold for the optical system of the secondembodiment of FIGS. 16-18. It is only necessary that these conditionsare satisfied in at least one zoom state.

In the second embodiment, the values of the focal length f in each ofConditions (3), (3′), and (3″), as set forth in the numerical data, are4.4 mm (wide-angle)˜13.2 mm (telephoto) and 7.6 mm (middle). The valueof the maximum amount of deformation md (mm) of the variable mirror isequal to that of the amount of decentration Z of the eighth surface. Thevalue of the area Sm of the optically effective reflecting surface ofthe variable mirror in Conditions (4) and (4′) is 69.08 mm². The valueof the voltage Vm applied to the deformable mirror in Conditions (5) and(5′) is in the range of 0 to 200 V, depending on the state. The value ofthe power φDM of the deformable mirror in Conditions (6), (6′), and (6″)is ½ (C4+C6). Also, the amount φDMx is C4 and φDMy is C6. The value ofthe focal length f 1 of the lens unit with negative power placed on theobject side of the variable mirror is −8.003. The value of the bendingangle θ of the axial chief ray of the deformable mirror in Conditions(8) and (8′) is 90.6°. The magnifications β1 of the lens unit rangingfrom an optical surface situated immediately behind the deformablemirror to the last surface in Conditions (9) and (9′) are −0.550 at thewide-angle position, −0.950 at the middle position, and −1.649 at thetelephoto position. The overall length Cj of the optical system inConditions (10), (10′), and (10″) is 56.78 mm. As mentioned above, it isonly necessary that individual conditions of the present invention aresatisfied in at least one state.

Subsequently, values of parameters of Conditions (3), (4), (6), (7),(9), and (10) are listed in Tables 2-6 and those of Conditions (11) and(12) are listed in Tables 7-10. TABLE 2 Condition State 1 State 2 State3 Object distance Wide-angle Middle Telephoto ∞ allowance ∞ allowance ∞allowance φDMx (power x) 0.000 × 10⁰ 0.000 × 10⁰ 0.000 × 10⁰ [l/mm] φDMy(power y) 0.000 × 10⁰ 0.000 × 10⁰ 0.000 × 10⁰ [l/mm] φDM 0.000 × 10⁰0.000 × 10⁰ 0.000 × 10⁰ md (the amount 0 0 0 of deformation) [mm] β1(magnification (9) −0.550 −0.950 −1.649 of rear lens unit) f (focallength) 4.4 7.6 13.2 [mm] Cj (overall length 56.78 56.78 56.78 ofoptical system) [mm] Sm (mirror area) 69.08 69.08 69.08 [mm²] f1 (focallength of −8.003 −8.003 −8.003 front lens unit) [mm] |md/f| (3) 0.000 ×10⁰ 0.000 × 10⁰ 0.000 × 10⁰ md²/Sm (4) 0 0 0 |φDM × f| (6) 0.000 × 10⁰0.000 × 10⁰ 0.000 × 10⁰ f1/f (7) −1.819 −1.053 −0.606 Cj/f (10) 12.9057.471 4.302

TABLE 3 Condition State 4 State 5 State 6 Object distance Wide-angle ∞Middle ∞ Telephoto ∞ φDMx (power x) [l/mm] −5.8995 × 10⁻⁴ −2.2653 × 10⁻⁴−1.0629 × 10⁻⁴ φDMy (power y) [l/mm] −2.9424 × 10⁻⁴ −1.1179 × 10⁻⁴−5.1178 × 10⁻⁵ φDM −4.4210 × 10⁻⁴ −1.6916 × 10⁻⁴ −7.8734 × 10⁻⁵ md (theamount of 0.00757 0.0028 0.00119 deformation) [mm] β1 (magnification of(9) −0.550 −0.950 −1.649 rear lens unit) f (focal length) [mm] 4.4 7.613.2 Cj (overall length of 56.78 56.78 56.78 optical system) [mm] Sm(mirror area) [mm²] 69.08 69.08 69.08 f1 (focal length of −8.003 −8.003−8.003 front lens unit) [mm] |md/f| (3) 1.7205 ×    3.6842 ×     9.0152× 10⁻⁵ md²/Sm (4) 8.29544 × 10⁻⁷ 1.13492 × 10⁻⁷ 2.04994 × 10⁻⁸ |φDM × f|(6) −1.9452 × 10⁻³ −1.2856 × 10⁻³ −1.0393 × 10⁻³ f1/f (7) −1.819 −1.053−0.606 Cj/f (10) 12.905 7.471 4.302

TABLE 4 Condition State 7 State 8 State 9 Object distance Wide-angleMiddle Telephoto 300 mm 300 mm 300 mm φDMx (power x) [l/mm] −8.9987 ×10⁻⁴ −5.5202 × 10⁻⁴ −4.4543 × 10⁻⁴ φDMy (power y) [l/mm] −4.6031 × 10⁻⁴−2.8215 × 10⁻⁴ −2.3298 × 10⁻⁴ φDM −6.8009 × 10⁻⁴ −4.1709 × 10⁻⁴ −3.3921× 10⁻⁴ md (the amount of 0.0127 0.00836 0.00675 deformation) [mm] β1(magnification of (9) −0.550 −0.950 −1.649 rear lens unit) f (focallength) [mm] 4.4 7.6 13.2 Cj (overall length of 56.78 56.78 56.78optical system) [mm] Sm (mirror area) [mm²] 69.08 69.08 69.08 f1 (focallength of −8.003 −8.003 −8.003 front lens unit) [mm] |md/f| (3) 2.8864 ×   1.1000 ×    5.1136 ×    md²/Sm (4) 2.33483 × 10⁻⁶ 1.01172 × 10⁻⁸6.59561 × 10⁻⁷ |φDM × f| (6) −2.9924 × 10⁻³ −3.1698 × 10⁻³ −4.4775 ×10⁻³ f1/f (7) −1.819 −1.053 −0.606 Cj/f (10) 12.905 7.471 4.302

TABLE 5 Condition State 10 State 11 State 12 Object distance Wide-angleMiddle Telephoto 300 mm 300 mm 300 mm allowance allowance allowance φDMx(power x) [l/mm] −1.4304 × 10⁻³ −7.6639 × 10⁻⁴ −5.4800 × 10⁻⁴ φDMy(power y) [l/mm] −7.4243 × 10⁻⁴ −3.9897 × 10⁻⁴ −2.8654 × 10⁻⁴ φDM−1.0864 × 10⁻³ −5.8268 × 10⁻⁴ −4.1727 × 10⁻⁴ md (the amount of 0.020750.01146 0.00826 deformation) [mm] β1 (magnification of (9) −0.550 −0.950−1.649 rear lens unit) f (focal length) [mm] 4.4 7.6 13.2 Cj (overalllength of 56.78 56.78 56.78 optical system) [mm] Sm (mirror area) [mm²]69.08 69.08 69.08 f1 (focal length of −8.003 −8.003 −8.003 front lensunit) [mm] |md/f| (3) 4.7159 ×    1.5079 ×     6.2576 × 10⁻⁴ md²/Sm (4)6.23281 × 10⁻⁸ 1.90115 × 10⁻⁶ 9.87661 × 10⁻⁷ |φDM × f| (6) −4.7802 ×10⁻³ −4.4284 × 10⁻³ −5.5080 × 10⁻³ f1/f (7) −1.819 −1.053 −0.606 Cj/f(10) 12.905 7.471 4.302

TABLE 6 Condition State 13 Object distance Telephoto electronic zoomφDMx (power x) −2.7203 × 10⁻⁴ [l/mm] φDMy (power y) −1.3596 × 10⁻⁴[l/mm] φDM −2.0400 × 10⁻⁴ md (the amount of 0.00377 deformation) [mm] β1(magnification of (9) −1.649 rear lens unit) f (focal length) 13.2 [mm]Cj (overall length of 56.78 optical system) [mm] Sm (mirror area) 69.08[mm²] f1 (focal length of −8.003 front lens unit) [mm] |md/f| (3) 2.8561×    md²/Sm (4) 2.05746 × 10⁻⁷ |φDM × f| (6) −2.6927 × 10⁻³ f1/f (7)−0.606 Cj/f (10) 4.302

TABLE 7 Lens No. (in order from the object side) 1 2 3 δ [mm] 0.06 0−0.05 |δ/f| Wide-angle 0.013636364 0 0.011363636 Middle 0.007894737 00.006578947 Telephoto 0.004545455 0 0.003787879 ε [deg] −0.76 0 0 |ε/f|Wide-angle 0.172727273 0 0 Middle 0.1 0 0 Telephoto 0.057575758 0 0

TABLE 8 Lens No. (in order from the object side) 4 5 6 δ [mm] −0.05 0.070.07 |δ/f| Wide-angle 0.011363636 0.015909091 0.015909091 Middle0.006578947 0.009210526 0.009210526 Telephoto 0.003787879 0.0053030300.005303030 ε [deg] 0 0 0 |ε/f| Wide-angle 0 0 0 Middle 0 0 0 Telephoto0 0 0

TABLE 9 Lens No. (in order from the object side) 7 8 9 δ [mm] −0.01 0 0|δ/f| Wide-angle 0.002272727 0 0 Middle 0.001315789 0 0 Telephoto0.000757576 0 0 ε [deg] 0 0 0 |ε/f| Wide-angle 0 0 0 Middle 0 0 0Telephoto 0 0 0

TABLE 10 Lens No. (in order from the object side) 10 Imaging surface δ[mm] 0.19 0 |δ/f| Wide-angle 0.043181818 0 Middle 0.025 0 Telephoto0.014393939 0 ε [deg] 0 1.15 |ε/f| Wide-angle 0 0.261363636 Middle 00.151315789 Telephoto 0 0.087121212

In the first and second embodiments, reference has been made to theoptical system using the deformable mirror. However, even in the opticalsystem using a planar mirror or curved mirror whose shape is notchanged, instead of the deformable mirror, the above conditions andlimitations may be applied unless otherwise specified. This is becausethe merit of compactness in a path-bending optical system using themirror is held as it is.

In the first and second embodiments, the optical system designed to havethe reflecting surface in the lens unit has been described. However,when the optical system with no reflecting surface is constructed byusing a variable optical-property element, for example, a variablefocal-length lens, effects of compactness, a cost reduction, powersaving, and operation noiselessness can be obtained. In addition, thevariable focal-length mirror with no deformable surface may be used inthe above embodiments. Also, the variable focal-length mirror is a kindof variable mirror. For the variable focal-length mirror, one examplewill be described later with reference to FIG. 46.

The above optical system is applicable to a film camera, a digitalcamera, a TV camera, a camera for personal digital assistants, animaging device of a mobile phone, a monitoring camera, a robot's eye,and an electronic endoscope.

In the above description, the imaging optical system is assumed as theoptical system, but the optical system can be used as a projectionoptical system, such as a projector, by replacing the object plane withthe image plane, and an optical apparatus using this projection opticalsystem can be fabricated.

Subsequently, a description will be given of the structural examples ofvariable optical-property elements, such as deformable mirrors andvariable focal-length lenses, applicable to the optical system used inthe optical apparatus of the present invention.

FIG. 21 shows an example of the deformable mirror constructed as thevariable optical-property element applicable to the optical system usedin the optical apparatus of the present invention. In FIG. 21, thedeformable mirror 409 includes the thin film (reflecting surface) 409 aof an aluminum coating formed on the deforming substrate 409 j; theplurality of electrodes 409 b in which the periphery of the three-layerstructure including the electrode 409 k provided beneath the substrate409 j is supported by the annular support 423 so that the electrodes 409b are spaced away from the electrode 409 k and are mounted to thesupport 423; a plurality of variable resistors 411 a connecting to theelectrodes 409 b and functioning as driving circuits; a power source 412connected between the electrode 409 k and the electrodes 409 b through avariable resistor 411 b and a power switch 413; and the arithmeticalunit 414 for controlling the resistance values of the plurality ofvariable resistors 411 a. The temperature sensor 415, the humiditysensor 416, and the range sensor 417 are connected to the arithmeticalunit 414, and as shown in the figure, these constitute one optical unit.Also, the deforming substrate 409 j may be the thin film or a plate.

The reflecting surface of the variable mirror need not necessarily beplanar, depending on the control of the arithmetical unit 414, and mayhave any shape such as a spherical or rotationally symmetricalaspherical surface; a spherical, planar, or rotationally symmetricalaspherical surface which has decentration with respect to the opticalaxis; an aspherical surface with symmetrical surfaces; an asphericalsurface with only one symmetrical surface; an aspherical surface with nosymmetrical surface; a free-formed surface; a surface with anondifferentiable point or line; etc. In general, such a surface isreferred as to an extended surface. By the reflecting surfaceconstructed of the thin film 409 a, a ray of light is reflected in thedirection of the arrow of the figure.

The thin film 409 a, like a membrane mirror set forth, for example, in“Handbook of Microlithography, Micromachining and Microfabrication”, byP. Rai-Choudhury, Volume 2: Micromachining and Microfabrication, p. 495,FIG. 8.58, SPIE PRESS, or Optics Communication, Vol. 140, pp. 187-190,1997, is such that when voltages are applied between the plurality ofelectrodes 409 b and the electrode 409 k, the thin film 409 a isdeformed by the electrostatic force and its surface profile is changed.Also, it is only necessary that the profile of the electrodes 409 b, forexample, as shown in FIG. 23 or 24, is selected to have a concentric orrectangular division pattern in accordance with the deformation of thethin film 409 a.

As mentioned above, the configuration of the thin film 409 a functioningas the reflecting surface is controlled in such a way that theresistance values of the variable resistors 411 a are changed by signalsfrom the arithmetical unit 414 to optimize imaging performance. Signalscorresponding to ambient temperature and humidity and a distance to theobject are input into the arithmetical unit 414 from the temperaturesensor 415, the humidity sensor 416, and the range sensor 417. Inaccordance with these input signals, the arithmetical unit 414 outputssignals for determining the resistance values of the variable resistors411 a so that voltages governing the configuration of the thin film 409a are applied to the electrodes 409 b by the command of the imageprocessor 303 for the ambient temperature and humidity conditions, thedistance to the object, and the electronic zoom. Thus, since the thinfilm 409 a is deformed with the voltages applied to the electrodes 409b, that is, the electrostatic forces, it assumes various shapesincluding an aspherical surface, according to circumstances. The rangesensor 417 need not necessarily be used, and in this case, it is onlynecessary that the object distance is calculated and the variable mirroris deformed so that a high-frequency component of an image signal from asolid-state image sensor 408 is roughly maximized. When the variablemirror 409 is made by using lithography, high fabrication accuracy andgood quality are easily obtained.

When the deforming substrate 409 j is made of synthetic resin, such aspolyimide or the trade name, Cytop (made by ASAHI GLASS CO., LTD), itcan be considerably deformed even at a low voltage, which isadvantageous.

In FIG. 21, the thin film 409 a of the reflecting surface and thedeforming electrode 409 k sandwiching the deforming substrate 409 jbetween them are integrally constructed, and thus there is the meritthat some manufacturing methods can be chosen. The thin film 409 a ofthe reflecting surface may be configured as a conductive thin film. Bydoing so, the thin film 409 a can also be used as the deformingelectrode 409 k. This brings about the merit that the structure issimplified because both are configured into one unit

It is favorable that the profile of the reflecting surface of thevariable mirror is a free-formed surface. This is because correction foraberration can be facilitated, which is advantageous.

Also, although in FIG. 21 the arithmetical unit 414, the temperaturesensor 415, the humidity sensor 416, and the range sensor 417 areprovided so that the variable mirror 409 compensates for the changes ofthe temperature, the humidity, and the object distance, the presentinvention is not limited to this construction. That is, the arithmeticalunit 414, the temperature sensor 415, the humidity sensor 416, and therange sensor 417 may be eliminated so that the variable mirror 409compensates for only a change of an observer's diopter.

FIG. 22 shows another example of the variable mirror 409. In thevariable mirror of this example, a piezoelectric element 409 c isinterposed between the thin film 409 a of the reflecting surface and theelectrodes 409 b, and these are placed on the support 423. A voltageapplied to the piezoelectric element 409 c is changed in accordance witheach of the electrodes 409 b, and thereby the piezoelectric element 409c causes expansion and contraction which are partially different so thatthe shape of the thin film 409 a can be changed. The configuration ofthe electrodes 409 b, as illustrated in FIG. 23, may have a concentricdivision pattern, or as in FIG. 24, may be a rectangular divisionpattern. As other patterns, proper configurations can be chosen. In FIG.22, reference numeral 424 represents a shake sensor connected to thearithmetical unit 414. The shake sensor 424, for example, detects theshake of a digital camera when the optical apparatus mentioned above isused in the digital camera, and changes the voltages applied to theelectrodes 409 b through the arithmetical unit 414 and driving circuits411 housing variable resistors in order to deform the thin film 409 a soas to compensate for the blurring of an image caused by the shake. Atthis time, signals from the temperature sensor 415, the humidity sensor416, and range sensor 417 are taken into account simultaneously, andfocusing and compensation for temperature and humidity are performed. Inthis case, stress is applied to the thin film 409 a by the deformationof the piezoelectric element 409 c, and hence it is good practice todesign the thin film 409 a so that it has a moderate thickness and aproper strength.

The driving circuits 411 are not limited to the construction that aplurality of circuits are arranged in accordance with the number of theelectrodes 409 b, and like the driving circuit 304 shown in FIG. 1, maybe constructed so that the plurality of electrodes 409 b are controlledby a single driving circuit.

FIG. 25 shows still another example of the variable mirror. The variablemirror of this example is constructed with two piezoelectric elements409 c and 409 c′ interposed between the thin film 409 a and theelectrodes 409 b and made with substances having piezoelectriccharacteristics which are reversed in direction. Specifically, thepiezoelectric elements 409 c and 409 c′ are made with ferroelectriccrystals and are arranged so that their crystal axes are reversed indirection with respect to each other. In this case, the piezoelectricelements 409 c and 409 c′ expand or contract in a reverse direction whenvoltages are applied, and thus there is the advantage that a force fordeforming the thin film 409 a becomes stronger than in the single layerstructure of FIG. 22, and as a result, the shape of the mirror surfacecan be considerably changed.

For substances used for the piezoelectric elements 409 c and 409 c′, forexample, there are piezoelectric substances such as barium titanate,Rochelle salt, quartz crystal, tourmaline, KDP, ADP, and lithiumniobate; polycrystals or crystals of the piezoelectric substances;piezoelectric ceramics such as solid solutions of PbZrO₃ and PbTiO₃;organic piezoelectric substances such as PVDF; and other ferroelectrics.In particular, the organic piezoelectric substance has a small value ofYoung's modulus and brings about a considerable deformation at a lowvoltage, which is favorable. When these piezoelectric elements are used,it is also possible to properly deform the thin film 409 a in each ofthe above examples if their thicknesses are made uneven.

As materials of the piezoelectric elements 409 c and 409 c′,high-polymer piezoelectrics such as polyurethane, silicon rubber,acrylic elastomer, PZT, PLZT, and PVDF; vinylidene cyanide copolymer;and copolymer of vinylidene fluoride and trifluoroethylene are used.

The use of an organic substance, synthetic resin, or elastomer, having apiezoelectric property, is favorable because it brings about aconsiderable deformation of the surface of the variable mirror

When an electrostrictive substance, for example, acrylic elastomer orsilicon rubber, is used for the piezoelectric element 409 c shown inFIGS. 22 and 26, the piezoelectric element 409 c, instead of the singlelayer structure, as indicated by a broken line in FIG. 22, may have thetwo-layer structure in which a substrate 409 c-1 is cemented to anelectrostrictive substance 409 c-2.

FIG. 26 shows another example of the variable mirror 409. The variablemirror of this example is designed so that the piezoelectric element 409c is sandwiched between the thin film 409 a and an electrode 409 d, andthese are placed on the support 423. Voltages are applied to thepiezoelectric element 409 c between the thin film 409 a and theelectrode 409 d through a driving circuit 425 a controlled by thearithmetical unit 414. Furthermore, apart from this, voltages are alsoapplied to the electrodes 409 b provided on the support 423, throughdriving circuits 425 b controlled by the arithmetical unit 414.Therefore, in this example, the thin film 409 a can be doubly deformedby electrostatic forces due to the voltages applied between the thinfilm 409 a and the electrode 409 d and applied to the electrodes 409 b.There are advantages that various deformation patterns can be providedand the response is quick, compared with any of the above examples.

By changing the signs of the voltages applied between the thin film 409a and the electrode 409 d, the variable mirror can be deformed intoeither a convex or concave surface. In this case, a considerabledeformation may be performed by a piezoelectric effect, while a slightshape change may be carried out by the electrostatic force.Alternatively, the piezoelectric effect may be chiefly used for thedeformation of the convex surface, while the electrostatic force may beused for the deformation of the concave surface. Also, the electrode 409d may be constructed as a plurality of electrodes like the electrodes409 b. This state is shown in FIG. 26. In the present invention, all ofthe piezoelectric effect, the electrostrictive effect, andelectrostriction are generally called the piezoelectric effect. Thus, itis assumed that the electrostrictive substance comes into the categoryof the piezoelectric substance.

FIG. 27 shows another example of the variable mirror 409. The variablemirror of this example is designed so that the shape of the reflectingsurface can be changed by utilizing an electromagnetic force. Apermanent magnet 426 is fixed on the bottom surface inside the support423, and the periphery of a substrate 409 e made with silicon nitride orpolyimide is mounted and fixed on the top surface thereof. The thin film409 a with the coating of metal, such as aluminum, is deposited on thesurface of the substrate 409 e, thereby constituting the variable mirror409.

Below the substrate 409 e, a plurality of coils 427 are fixedly mountedand connected to the arithmetical unit 414 through driving circuits 428.In accordance with output signals from the arithmetical unit 414corresponding to changes of the optical system obtained at thearithmetical unit 414 by signals from the sensors 415, 416, 417, and 424and the image processor 303 for the electronic zoom, proper electriccurrents are supplied from the driving circuits 428 to the coils 427. Atthis time, the coils 427 are repelled or attracted by theelectromagnetic force with the permanent magnet 426 to deform thesubstrate 409 e and the thin film 409 a functioning as the reflectingsurface.

In this case, a different amount of current can also be caused to flowthrough each of the coils 427. A single coil 427 may be used. Thepermanent magnet 426 may be mounted on the lower surface of thesubstrate 409 e so that the coils 427 are arranged on the bottom side inthe support 423. It is desirable that the coils 427 are made by alithography process. A ferromagnetic iron core may be encased in each ofthe coils 427.

In this case, each of the coils 427, as illustrated in FIG. 28, can bedesigned so that a coil density varies with the place like a coil 428′,and thereby a desired deformation is brought to the substrate 409 e andthe thin film 409 a. A single coil 427 may be used, or a ferromagneticiron core may be encased in each of the coils 427.

FIG. 29 shows another example of the variable mirror 409. In thevariable mirror of this example, the substrate 409 e is made with aferromagnetic such as iron, and the thin film 409 a of the reflectingfilm is made with aluminum. In this case, since even though the coilsare not provided beneath the substrate 409 e, the thin film 409 a can bedeformed by the magnetic force, the structure is simplified and themanufacturing cost can be reduced. If the power switch 413 is replacedwith a changeover and power on-off switch, the directions of currentsflowing through the coils 427 can be changed, and the configurations ofthe substrate 409 e and the thin film 409 a can be changed at will. FIG.30 shows an example of an array of the coils 427 of this example. FIG.31 shows another example of the array of the coils 427. These arrays arealso applicable to the example of FIG. 27. FIG. 32 shows an array of thepermanent magnets 426 suitable for the case where the coils 427, asshown in FIG. 31, are radially arrayed. Specifically, when thebar-shaped permanent magnets 426, as shown in FIG. 32, are radiallyarrayed, a delicate deformation can be provided to the substrate 409 eand the thin film 409 a in contrast with the example of FIG. 27. Asmentioned above, when the electromagnetic force is used to deform thesubstrate 409 e and the thin film 409 a (in the examples of FIGS. 27 and29), there is the advantage that they can be driven at a lower voltagethan in the case where the electrostatic force is used.

Some examples of the variable mirrors have been described, but as shownin the example of FIG. 26, at least two kinds of forces may be used inorder to change the shape of the mirror constructed with a thin film.Specifically, at least two of the electrostatic force, electromagneticforce, piezoelectric effect, magnetrostriction, pressure of a fluid,electric field, magnetic field, temperature change, and electromagneticwave, may be used simultaneously to deform the thin film constitutingthe reflecting surface. That is, when at least two different drivingtechniques are used to make the variable optical-property element, aconsiderable deformation and a slight deformation can be realizedsimultaneously and a mirror surface with a high degree of accuracy canbe obtained.

FIG. 33 shows an imaging system which uses the variable mirror 409applicable to the optical apparatus of another example of the presentinvention and is used, for example, in a digital camera of a mobilephone, a capsule endoscope, an electronic endoscope, a digital camerafor personal computers, or a digital camera for PDAs. In the imagingsystem of this example, one imaging unit 104 is constructed with thedeformable mirror 409, the lens 902, the solid-state image sensor 408,and a control system 103. The imaging unit 104 of this example isdesigned so that light from an object passing through the lens 902 iscondensed by the variable mirror 409 and is imaged on the solid-stateimage sensor 408. The variable mirror 409 is a kind of variableoptical-property element and is also referred to as the variablefocal-length mirror.

According to this example, even when the object distance is changed, thevariable mirror 409 is deformed and thereby the object can be broughtinto a focus. The example need not move the lens 902 by using a motorand excels in compact and lightweight design and low power consumption.The imaging unit 104 can be used in any of the examples as the imagingoptical system of the present invention. When a plurality of variablemirrors 409 are used, an optical system, such as a zoom imaging opticalsystem or a variable magnification imaging optical system, can beconstructed.

In FIG. 33, an example of a control system is cited which includes theboosting circuit of a transformer using coils in the control system 103.In particular, the use of a laminated piezoelectric transformer isfavorable because a compact design can be achieved. The boosting circuitcan be used in the variable mirror or the variable focal-length lenswhich uses electricity, and is particularly useful for the variablemirror or the variable focal-length lens which utilizes theelectrostatic force or the piezoelectric effect. In order to use thevariable mirror 409 for focusing, it is only necessary, for example, toform an object image on the solid-state image sensor 408 and to find astate where the high-frequency component of the object image ismaximized while changing the focal length of the variable mirror 409. Inorder to detect the high-frequency component, it is only necessary, forexample, to connect a processor including a microcomputer to thesolid-state image sensor 408 and to detect the high-frequency componenttherein.

FIG. 34 shows another example of the variable mirror. In this figure, avariable mirror 188 is constructed so that a fluid 161 is taken in andout by a micropump 180 to deform a mirror surface which is configuredwith a film extended on the upper surface of a support 189 a. Accordingto this example, there is the merit that the mirror surface can beconsiderably deformed. In this figure, reference numeral 168 denotes acontrol device controlling the amount of the fluid 161 in the support189 a, together the micropump 180. The control device 168 and themicropump 180 are to control the deformation of a film 189, and thuscorrespond to the driving circuit 304. The micropump 180 is asmall-sized pump, for example, made by a micromachining technique and isconstructed so that it is operated with an electric power. As examplesof pumps made by the micromachining technique, there are those which usethermal deformations, piezoelectric substances, and electrostaticforces.

FIG. 35 shows an example of the micropump 180 of FIG. 34. In themicropump 180 of this example, a vibrating plate 181 is vibrated by theelectrostatic force or the electric force of the piezoelectric effect.In FIG. 35, a case where the vibrating plate is vibrated by theelectrostatic force is shown and reference numerals 182 and 183represent electrodes. Dotted lines indicate the vibrating plate 181where it is deformed. When the vibrating plate 181 is vibrated, twovalves 184 and 185 are opened and closed to feed the fluid 161 from theright to the left.

In the variable mirror 188 shown in FIG. 34, the film 189 constitutingthe reflecting surface is deformed into a concave or convex surface inaccordance with the amount of the fluid 161, thereby functioning as thevariable mirror. An organic or inorganic substance, such as silicon oil,air, water, or jelly, can be used as the fluid.

In the variable mirror or the variable focal-length lens which uses theelectrostatic force or the piezoelectric effect, a high voltage issometimes required for drive. In this case, for example, as shown inFIG. 33, it is desirable that the boosting transformer or thepiezoelectric transformer is used to constitute the control system.

The provision of the thin film 409 a or the film 189 which constitutesthe reflecting surface on a member which is not deformed like the upperportion of the annular member of the support 423 or 189 a is convenientbecause it can be used as a reference surface when the profile of thereflecting surface of the variable mirror is measured by aninterferometer.

FIG. 36 shows the principle structure of the variable focal-length lensthat a part of lenses or a lens unit constituting the optical systemapplicable to the optical apparatus of the present invention is replacedwith the variable focal-length lens and thereby zooming of the lenses orthe lens unit in the direction of the optical axis becomes unnecessary.A variable focal-length lens 511 includes a first lens 512 a having lenssurfaces 508 a and 508 b as a first surface and a second surface,respectively; a second lens 512 b having lens surfaces 509 a and 509 bas a third surface and a fourth surface, respectively; and a third lens512 c constructed with a macromolecular dispersed liquid crystal layer514 sandwiched between the first and second lenses through transparentelectrodes 513 a and 513 b. Incident light is converged through thefirst, third, and second lenses 512 a, 512 c, and 512 b. The transparentelectrodes 513 a and 513 b are connected to an alternating-current powersupply 516 through a switch 515 so that an alternating-current voltageis selectively applied to the macromolecular dispersed liquid crystallayer 514. The macromolecular dispersed liquid crystal layer 514 iscomposed of a great number of minute macromolecular cells 518, eachhaving any shape, such as a sphere or polyhedron, and including liquidcrystal molecules 517. The volume of each cell is equal to the sum ofvolumes occupied by macromolecules and the liquid crystal molecules 517which constitute the macromolecular cells 518.

Here, for the size of each of the macromolecular cells 518, for example,in the case of a sphere, when an average diameter is denoted by D andthe wavelength of light used is denoted by λ, the average diameter D ischosen to satisfy the following condition:2 nm≦D≦λ/5  (13)That is, the size of each of the liquid crystal molecules 517 is atleast about 2 nm and thus the lower limit of the average diameter D isset to 2 nm or larger. The upper limit of the diameter D depends on athickness t of the macromolecular dispersed liquid crystal layer 514 inthe direction of the optical axis of the variable focal-length lens 511.However, if the diameter is larger than the wavelength λ, a differencein refractive index between the macromolecule and the liquid crystalmolecule 517 will cause light to be scattered at the interface of themacromolecular cell 518 and will render the liquid crystal layer 514opaque. Hence, the upper limit of the diameter D, as described later,should preferably be λ/5 or less. A high degree of accuracy is notnecessarily required, depending on an optical product using the variablefocal-length lens. In this case, the diameter D below the value of thewavelength λ is satisfactory. Also, the transparency of themacromolecular dispersed liquid crystal layer 514 deteriorates withincreasing thickness t.

In the liquid crystal molecules 517, for example, uniaxial nematicliquid crystal molecules are used. The index ellipsoid of each of theliquid crystal molecules 517 is as shown in FIG. 37. That is,n_(ox)=n_(oy)=n_(o)  (14)where n_(o) is the refractive index of an ordinary ray, and n_(ox) andn_(oy) are refractive indices in directions perpendicular to each otherin a plane including ordinary rays.

Here, in the case where the switch 515, as shown in FIG. 36 is turnedoff, that is, the electric field is not applied to the liquid crystallayer 514, the liquid crystal molecules 517 are oriented in variousdirections, and thus the refractive index of the liquid crystal layer514 relative to incident light becomes high to provide a lens withstrong refracting power. In contrast to this, when the switch 515, asshown in FIG. 38, is turned on and the alternating-current voltage isapplied to the liquid crystal layer 514, the liquid crystal molecules517 are oriented so that the major axis of the index ellipsoid of eachliquid crystal molecule 517 is parallel with the optical axis of thevariable focal-length lens 511, and hence the refractive index becomeslower to provide a lens with weaker refracting power.

The voltage applied to the macromolecular dispersed liquid crystal layer514, for example, as shown in FIG. 39, can be changed stepwise orcontinuously by the use of a variable resistor 519. By doing so, as theapplied voltage becomes high, the liquid crystal molecules 517 areoriented so that the major axis of the index ellipsoid of each liquidcrystal molecule 517 becomes progressively parallel with the opticalaxis of the variable focal-length lens 511, and thus the refractiveindex can be changed stepwise or continuously.

Here, in the case of FIG. 36, that is, in the case where the voltage isnot applied to the macromolecular dispersed liquid crystal layer 514,when the refractive index in the direction of the major axis of theindex ellipsoid, as shown in FIG. 37, is denoted by n_(z), an averagerefractive index n_(LC)′ of the liquid crystal molecules 517 is roughlygiven by(n _(ox) +n _(oy) +n _(z))/3≡n _(LC)′  (15)Also, when the refractive index n_(z) is expressed as a refractive indexn_(e) of an extraordinary ray, an average refractive index n_(LC) of theliquid crystal molecules 517 where Equation (14) is established is givenby(2n _(o) +n _(e))/3≡n _(LC)  (16)In this case, when the refractive index of each of the macromoleculesconstituting the macromolecular cells 518 is represented by n_(p) andthe ratio of volume between the liquid crystal layer 514 and the liquidcrystal molecules 517 is represented by if, a refractive index n_(A) ofthe liquid crystal layer 514 is given from the Maxwell-Garnet's law asn _(A) =ff·n _(LC)′+(1−ff)n _(p)  (17)

Thus, as shown in FIG. 39, when the radii of curvature of the innersurfaces of the lenses 512 a and 512 b, that is, the surfaces on theside of the liquid crystal layer 514, are represented by R₁ and R₂, afocal length f₁ of the third lens 512 c constructed with the liquidcrystal layer 514 is given by1/f ₁=(n _(A)−1)(1/R ₁−1/R ₂)  (18)Also, when the center of curvature is located on the image side, it isassumed that each of the radii of curvature R₁ and R₂ is positive.Refraction caused by the outer surface of each of the lenses 512 a and512 b is omitted. That is, the focal length of the lens 512 cconstructed with only the liquid crystal layer 514 is given by Equation(18).

When the average refractive index of ordinary rays is expressed as(n _(ox) +n _(oy))/2=n _(o)′  (19)a refractive index n_(B) of the liquid crystal layer 514 in the case ofFIG. 38, namely, in the case where the voltage is applied to the liquidcrystal layer 514, is given byn _(B) =ff·n _(o)′+(1−ff)n _(p)  (20)and thus a focal length f₂ of the lens 512 c constructed with only theliquid crystal layer 514 in this case is given by1/f ₂=(n _(B)−1)(1/R ₁1/R ₂)  (21)Also, the focal length where a lower voltage than in FIG. 38 is appliedto the liquid crystal layer 514 takes a value between the focal lengthf₁ given by Equation (18) and the focal length f₂ by Equation (21).

From Equations (18) and (21), a change rate of the focal length of thelens constructed with the liquid crystal layer 514 is given by|(f ₂ −f ₁)/f ₂|=|(n _(B) −n _(A))/(n _(A)−1)|  (22)

Thus, in order to increase the change rate, it is only necessary toincrease the value of |n_(B)−n_(A)|. Here,n _(B) −n _(A) =ff(n _(o) ′−n _(LC)′)  (23)and hence if the value of |n_(o)′−n_(LC)′| is increased, the change ratecan be raised. Practically, since the refractive index n_(B) of theliquid crystal layer 514 is about 1.3-2, the value of |n_(o)′−n_(LC)′|is chosen so as to satisfy the following condition:0.01≦n _(o) ′−n _(LC)′|≦10  (24)In this way, when ff=0.5, the focal length of the lens constructed withthe liquid crystal layer 514 can be changed by at least 0.5%, and thusan effective variable focal-length lens can be obtained. Also, the valueof |n_(o)′−n_(LC)′| cannot exceed 10 because of restrictions on liquidcrystal substances.

Subsequently, a description will be given of grounds for the upper limitof Condition (13). The variation of a transmittance τ where the size ofeach cell of a macromolecular dispersed liquid crystal is changed isdescribed in “Transmission variation using scattering/transparentswitching films” on pages 197-214 of “Solar Energy Materials and SolarCells”, Wilson and Eck, Vol. 31, Eleesvier Science Publishers B. v.,1993. In FIG. 6 on page 206 of this publication, it is shown that whenthe radius of each cell of the macromolecular dispersed liquid crystalis denoted by r, t=300 μm, ff=0.5, n_(p)=1.45, n_(LC)=1.585, and λ=500nm, the theoretical value of the transmittance τ is about 90% if r=5 nm(D=λ/50 and D·t=λ·6 μm, where D and λ are expressed in nanometers), andis about 50% if r=25 nm (D=λ/10).

Here, it is assumed that t=150 μm and the transmittance τ varies as theexponential function of the thickness t. The transmittance τ in the caseof t=150 μm is nearly 71% when r=25 nm (D=λ/10 and D·t=λ·15 μm).Similarly, in the case of t=75 μm, the transmittance τ is nearly 80%when r=25 nm (D=λ/10 and D·t=λ·7.5 μm).

From these results, the transmittance τ becomes at least 70-80% and theliquid crystal can be actually used as a lens, if the liquid crystalsatisfies the following condition:D·t≦λ·15 μm  (25)Hence, for example, in the case of t=75 μm, if D≦λ/5, a satisfactorytransmittance can be obtained.

The transmittance of the macromolecular dispersed liquid crystal layer514 is raised as the value of the refractive index n_(p) approaches thevalue of the refractive index n_(LC)′. On the other hand, if the valuesof the refractive indices n_(o)′ and n_(p) are different from eachother, the transmittance of the liquid crystal layer 514 will bedegraded. In FIGS. 36 and 38, the transmittance of the liquid crystallayer 514 is improved on an average when the liquid crystal layer 514satisfies the following equation:n _(p)=(n _(o) ′+n _(LC)′)/2  (26)

The variable focal-length lens 511 is used as a lens, and thus in bothFIGS. 36 and 38, it is desirable that the transmittances are almost thesame and high. For this, although there are limits to the substances ofthe macromolecules and the liquid crystal molecules 517 constituting themacromolecular cells 518, it is only necessary, in practical use, tosatisfy the following condition:n_(o)′≦n_(p)≦n_(LC)′  (27)

When Equation (26) is satisfied, Condition (25) is moderated and it isonly necessary to satisfy the following condition:D·t≦λ·60 μm  (28)It is for this reason that, according to the Fresnel's law ofreflection, the reflectance is proportional to the square of thedifference of the refractive index, and thus the reflection of light atthe interfaces between the macromolecules and the liquid crystalmolecules 517 constituting the macromolecular cells 518, that is, areduction in the transmittance of the liquid crystal layer 514, isroughly proportional to the square of the difference in refractive indexbetween the macromolecules and the liquid crystal molecules 517.

In the above description, reference has been made to the case wheren_(o)′≈1.45 and n_(LC)′≈1.585, but in a more general formulation, it isonly necessary to satisfy the following condition:D·t≦λ·15 μm·(1.585−1.45)²/(n _(u) −n _(p))²  (29)where (n_(u)−n_(p))² is a value when one of (n_(LC)′−n_(p))² and(n_(o)′−n_(p))² is larger than the other.

In order to largely change the focal length of the variable focal-lengthlens 511, it is favorable that the ratio ff is as high as possible, butin the case of ff=1, the volume of the macromolecule becomes zero andthe macromolecular cells 518 cease to be formable. Thus, it is necessaryto satisfy the following condition:0.1≦ff≦0.999  (30)

On the other hand, the transmittance τ improves as the ratio ff becomeslow, and hence Condition (29) may be moderated, preferably, as follows:4×10⁻⁶[μm]² ≦D·t≦λ·45 μm·(1.585−1.45)²/(n _(u) −n _(p))²  (31)Also, the lower limit of the thickness t, as is obvious from FIG. 36,corresponds to the diameter D, which is at least 2 nm as describedabove, and therefore the lower limit of D·t becomes (2×10⁻³ μm)², namely4×10⁻⁶ [μm]².

An approximation where the optical property of substance is representedby the refractive index is established when the diameter D is 5-10 nm orlarger, as set forth in “Iwanami Science Library 8, Asteroids arecoming”, T. Mukai, Iwanami Shoten, p. 58, 1994. If the value of thediameter D exceeds 500λ, the scattering of light will be changedgeometrically, and the scattering of light at the interfaces between themacromolecules and the liquid crystal molecules 517 constituting themacromolecular cells 518 is increased in accordance with the Fresnel'sequation of reflection. As such, in practical use, the diameter D mustbe chosen so as to satisfy the following condition:7 nm≦D≦500λ  (32)

FIG. 40 shows an imaging optical system using the variable focal-lengthlens 511 of FIG. 39 provided between an aperture stop 521 and the imagesensor in the optical apparatus of the present invention, for example,an example where the variable focal-length lens 511 is used in animaging optical system for digital cameras. In this imaging opticalsystem, an image of an object (not shown) is formed on a solid-stateimage sensor 523, such as a CCD, through the stop 521, the variablefocal-length lens 511, and a lens 522. Also, in FIG. 40, the liquidcrystal molecules are not shown.

According to such an imaging optical system, the alternating-currentvoltage applied to the macromolecular dispersed liquid crystal layer 514of the variable focal-length lens 511 is controlled by the variableresistor 519 to change the focal length of the variable focal-lengthlens 511. Whereby, without moving the variable focal-length lens 511 andthe lens 522 along the optical axis, it becomes possible to performcontinuous focusing with respect to the object distance, for example,from the infinity to 600 mm.

FIG. 41 shows one example of a variable focal-length diffraction opticalelement used so that the focal length of the imaging optical system canbe changed, like the variable focal-length lens of FIG. 39, in theoptical apparatus of the present invention. A variable focal-lengthdiffraction optical element 531 of this example includes a firsttransparent substrate 532 having a first surface 532 a and a secondsurface 532 b which are parallel with each other and a secondtransparent substrate 533 having a third surface 533 a which isconstructed with an annular diffraction grating of saw-like crosssection having the depth of a groove corresponding to the wavelength oflight and a fourth surface 533 b which is flat. Incident light emergesthrough the first and second transparent substrates 532 and 533. Betweenthe first and second transparent substrates 532 and 533, as in FIG. 36,the macromolecular dispersed liquid crystal layer 514 is sandwichedthrough the transparent electrodes 513 a and 513 b so that thetransparent electrodes 513 a and 513 b are connected to thealternating-current power supply 516 through the switch 515 and thealternating-current voltage is applied to the macromolecular dispersedliquid crystal layer 514.

In such a structure, when the grating pitch of the third surface 533 ais represented by p and an integer is represented by m, a ray of lightincident on the variable focal-length diffraction optical element 531 isdeflected by an angle θ satisfying the following equation:p sin θ=mλ  (33)and emerges therefrom. When the depth of the groove is denoted by h, therefractive index of the transparent substrate 533 is denoted by n₃₃, andan integer is denoted by k, a diffraction efficiency becomes 100% at thewavelength λ and the production of flare can be prevented by satisfyingthe following equations:h(n _(A) −n ₃₃)=mλ  (34)h(n _(B) −n ₃₃)=kλ  (35)

Here, the difference in both sides between Equations (34) and (35) isgiven byh(n _(A) −n _(B))=(m−k)λ  (36)Therefore, when it is assumed that λ=500 nm, n_(A)=1.55, and n_(B)=1.5,0.05 h=(m−k)·500 nmand when m=1 and k=0,h=10000 nm=10 μmIn this case, the refractive index n₃₃ of the transparent substrate 533is obtained as 1.5 from Equation (34). When the grating pitch p on theperiphery of the variable focal-length diffraction optical element 531is assumed to be 10 μm, θ≈2.87′ and a lens with an F-number of 10 can beobtained.

The variable focal-length diffraction optical element 531, whose opticalpath length is changed by the on-off operation of the voltage applied tothe liquid crystal layer 514, for example, can be used for focusadjustment in such a way that it is placed at a portion where the lightbeam of a lens system is not parallel, or can be used to change thefocal length of the entire lens system.

In this example, it is only necessary that Equations (34)-(36) are setin practical use to satisfy the following conditions:0.7 mλ≦h(n _(A) −n ₃₃)≦1.4 mλ  (37)0.7 kλ≦h(n _(A) −n ₃₃)≦1.4 kλ  (38)0.7(m−k)λ≦h(n _(A) −n _(B))≦1.4(m−k)λ  (39)

A variable focal-length lens using a twisted nematic liquid crystal alsofalls into the category of the present invention. FIGS. 42 and 43 showvariable focal-length spectacles 550 in this case. A variablefocal-length lens 551 has lenses 552 and 553, orientation films 539 aand 539 b provided through the transparent electrodes 513 a and 513 b,respectively, inside these lenses, and a twisted nematic liquid crystallayer 554 sandwiched between the orientation films. The transparentelectrodes 513 a and 513 b are connected to the alternating-currentpower supply 516 through the variable resistor 519 so that thealternating-current voltage is applied to the twisted nematic liquidcrystal layer 554.

In this structure, when the voltage applied to the twisted nematicliquid crystal layer 554 is increased, liquid crystal molecules 555, asillustrated in FIG. 43, exhibit a homeotropic orientation, in which therefractive index of the liquid crystal layer 554 is lower and the focallength is longer than in a twisted nematic state of FIG. 42 in which theapplied voltage is low.

A spiral pitch P of the liquid crystal molecules 555 in the twistednematic state of FIG. 42 must be made nearly equal to, or much smallerthan, the wavelength λ of light, and thus is set to satisfy thefollowing condition:2 nm≦P≦2λ/3  (40)

Also, the lower limit of this condition depends on the sizes of theliquid crystal molecules 555, while the upper limit is a value necessaryfor the behavior of the liquid crystal layer 554 as an isotropic mediumin a state of FIG. 42 when incident light is natural light. If the upperlimit of the condition is overstepped, the variable focal-length lens551 is changed to a lens in which the focal length varies with thedirection of deflection. Hence, a double image is formed and only ablurred image is obtained.

FIG. 44A shows an example of a variable deflection-angle prismapplicable to the optical system used in the optical apparatus of thepresent invention. A variable deflection-angle prism 561 includes afirst transparent substrate 562 on the entrance side, having a firstsurface 562 a and a second surface 562 b; and a second transparentsubstrate 563 like a plane-parallel plate on the exit side, having athird surface 563 a and a fourth surface 563 b. The inner surface (thesecond surface) 562 b of the transparent substrate 562 on the entranceside is configured into a Fresnel form, and the macromolecular dispersedliquid crystal layer 514, as in FIG. 36, is sandwiched between thistransparent substrate 562 and the transparent substrate 563 on the exitside through the transparent electrodes 513 a and 513 b. The transparentelectrodes 513 a and 513 b are connected to the alternating-currentpower supply 516 through the variable resistor 519. Whereby, thealternating-current voltage is applied to the liquid crystal layer 514so that a deflection angle θ of light transmitted through the variabledeflection-angle prism 561 is controlled. Also, in FIG. 44A, the innersurface 562 b of the transparent substrate 562 is configured into theFresnel form, but as shown in FIG. 44B, the inner surfaces of thetransparent substrates 562 and 563 may be configured like an ordinaryprism whose surfaces are relatively inclined, or may be configured likethe diffraction grating shown in FIG. 41. In the case of the latter,Equations (33)-(36) and Conditions (37)-(39) apply equally.

The variable deflection-angle prism 561 constructed mentioned above isused in each of the optical systems, for example, of TV cameras, digitalcameras, film cameras, or binoculars, and thereby can be effectivelyused for shake prevention. In this case, it is desirable that thedirection of refraction (deflection) of the variable deflection-angleprism 561 is vertical. In order to further improve its performance, itis desirable that two variable deflection-angle prisms 561 are arrangedso that the directions of deflection of the prisms 561 are varied and asshown in FIG. 45, the refraction angles are changed in vertical andlateral directions. Also, in FIGS. 44A, 44B, and 45, the liquid crystalmolecules are omitted.

FIG. 46 shows an example of a variable focal-length mirror used insteadof the variable mirror, that is, configured by providing a reflectingfilm on one surface of the variable focal-length lens, in the opticalsystem of the optical apparatus according to the present invention.

A variable focal-length mirror 565 of this example includes a firsttransparent substrate 566 having a first surface 566 a and a secondsurface 566 b, and a second transparent substrate 567 having a thirdsurface 567 a and a fourth surface 567 b. The first transparentsubstrate 566 is configured into a flat plate or lens shape to providethe transparent electrode 513 a on the inner surface (the secondsurface) 566 b. The second transparent substrate 567 is such that theinner surface (the third surface) 567 a is configured as a concavesurface, on which a reflecting film 568 is deposited, and thetransparent electrode 513 b is provided on the reflecting film 568.Between the transparent electrodes 513 a and 513 b, as in FIG. 36, themacromolecular dispersed liquid crystal layer 514 is sandwiched so thatthe transparent electrodes 513 a and 513 b are connected to thealternating-current power supply 516 through the switch 515 and thevariable resistor 519, and the alternating-current voltage is applied tothe macromolecular dispersed liquid crystal layer 514. Also, in FIG. 46,the liquid crystal molecules are omitted.

According to the above structure, since a ray of light incident from theside of the transparent substrate 566 is passed again through the liquidcrystal layer 514 by the reflecting film (reflecting surface) 568, thefunction of the liquid crystal layer 514 can be exercised twice, and thefocal position of reflected light can be shifted by changing the voltageapplied to the liquid crystal layer 514. In this case, the ray of lightincident on the variable focal-length mirror 565 is transmitted twicethrough the liquid crystal layer 514, and therefore when a thicknesstwice that of the liquid crystal layer 514 is represented by t, theconditions mentioned above can be used. Moreover, the inner surface ofthe transparent substrate 566 or 567, as shown in FIG. 41, can also beconfigured into a diffraction grating shape to reduce the thickness ofthe liquid crystal layer 514. This offers the advantage that the amountof scattered light can be decreased.

In the above description, in order to prevent the deterioration of theliquid crystal, the alternating-current power supply 516 is used as avoltage source to apply the alternating-current voltage to the liquidcrystal layer. However, a direct-current power supply is used andthereby a direct-current voltage can also be applied to the liquidcrystal. Techniques of shifting the orientation of the liquid crystalmolecules, in addition to changing the voltage, can be achieved bychanging the frequency of the electric field applied to the liquidcrystal, the strength and frequency of the magnetic field applied to theliquid crystal, and the temperature of the liquid crystal. In the abovedescription, some of macromolecular dispersed liquid crystals are closeto solids, rather than liquids. In this case, therefore, one of thelenses 512 a and 512 b, the transparent substrates 532 and 533, one ofthe lenses 552 and 553, the transparent substrate 563 in FIG. 44A, oneof the transparent substrates 562 and 563 in FIG. 44B, or one of thetransparent substrates 566 and 567, may be eliminated.

The optical element of the type that the focal length of the opticalelement is changed by altering the refracting index of a medium, such asthat described in FIGS. 36-46, has the merits that since the shape isnot changed, a mechanical design is easy and a mechanical structurebecomes simple.

FIG. 47 shows an example of an imaging optical system using a variablefocal-length lens 140 ahead of the image sensor 408 in the opticalapparatus of the present invention. The imaging optical system can beused as an imaging unit 141. In this example, a lens 102 and thevariable focal-length lens 140 constitute an imaging lens system. Thisimaging lens system and the image sensor 408 constitute the imaging unit141. The variable focal-length lens 140 is constructed with atransparent member 142; a soft transparent substance 143, such aspiezoelectric synthetic resin, enclosed between a pair of transparentelectrodes 145; and a light-transmitting fluid or a jelly-like substance144 sandwiched between the transparent member 142 and the transparentelectrode 145. As the fluid or the jelly-like substance 144, siliconoil, elastic rubber, jelly, or water can be used. The transparentelectrodes 145 are provided on both sides of the transparent substance143, and when voltages are applied through a circuit 103 to thetransparent electrodes 145, the transparent substance 143 is deformed bythe piezoelectric effect of the transparent substance 143 so that thefocal length of the variable focal-length lens 140 is changed. Thus,according to the example, even when the object distance is changed,focusing can be performed without moving the imaging optical system witha motor, and as such the example excels in compact and lightweightdesign and low power consumption.

Again, in FIG. 47, reference numerals 145 denotes transparent electrodesand numeral 146 denotes a cylinder for storing a fluid. For thetransparent substance 143, high-polymer piezoelectrics such aspolyurethane, silicon rubber, acrylic elastomer, PZT, PLZT, and PVDF;vinylidene cyanide copolymer; or copolymer of vinylidene fluoride andtrifluoroethylene is used.

The use of an organic substance, synthetic resin, or elastomer, having apiezoelectric property, is favorable because a considerable deformationof the surface of the variable focal-length lens 140 is brought about.It is good practice to use a transparent piezoelectric substance for thevariable focal-length lens 140.

In FIG. 47, instead of using the cylinder 146, the variable focal-lengthlens 140, as shown in FIG. 48, may be designed so that annularsupporting members 147 are provided at the position parallel with thetransparent member 142 and a distance between the transparent member 142and the supporting members 147 is maintained.

In FIG. 48, the transparent substance 143 enclosed between the pair ofelectrodes 143 and the fluid or the jelly-like substance 144 coveredwith a periphery-deformable member 148 are interposed between thesupporting members 147 and the transparent member 142. Even when thevoltage is applied to the transparent substance 143 and thereby thetransparent substance 143 is deformed, as shown in FIG. 49, thedeformable member 148 is deformed so that the entire volume of thevariable focal-length lens 140 is not changed. As such, the cylinder 146becomes unnecessary. Also, in FIGS. 48 and 49, the deformable member 148is made with an elastic body, accordion-shaped synthetic resin, ormetal.

In each of the examples shown in FIGS. 47 and 48, when a reverse voltageis applied, the transparent substance 143 is deformed in a reversedirection, and thus it is also possible to construct a concave lens.

Where an electrostrictive substance, for example, acrylic elastomer orsilicon rubber, is used for the transparent substance 143, it isdesirable that the transparent substance 143 is constructed so that thetransparent substrate and the electrostrictive substance are cemented toeach other.

FIG. 50 shows a variable focal-length lens 167 in which the fluid 161 istaken in and out by micropumps 160 to deform the lens surface, inanother example of the variable focal-length lens applicable to theimaging optical system of the optical apparatus according to the presentinvention.

Each of the micropumps 160 is a small-sized pump, for example, made by amicromachining technique and is constructed so that it is operated withan electric power. The fluid 161 is sandwiched between a transparentsubstrate 163 and a transparent elastic body 164. The elastic body 164constitutes a lens surface deformed by the fluid 161. In FIG. 50,reference numeral 165 represents a transparent substrate for protectingthe elastic body 164, but this substrate is not necessarily required. Asexamples of pumps made by the micromachining technique, there are thosewhich use thermal deformations, piezoelectric substances, andelectrostatic forces. It is also possible to use two micropumps, each ofwhich is the micropump 180 shown in FIG. 35, for example, as in themicropumps 160 used in the variable focal-length lens 167 of FIG. 50.

In the variable focal-length lens which uses the electrostatic force orthe piezoelectric effect, a high voltage is sometimes required fordrive. In this case, it is desirable that the boosting transformer orthe piezoelectric transformer is used to constitute the control system.In this case, when a laminated piezoelectric transformer is used, acompact design can be achieved.

FIG. 51 shows a variable focal-length lens 201 using a piezoelectricsubstance 200, in another example of a variable optical-property elementapplicable to the optical system of the optical apparatus according tothe present invention. The same substance as the transparent substance143 is used for the piezoelectric substance 200, which is provided on asoft transparent substrate 202. It is desirable that synthetic resin oran organic substance is used for the substrate 202.

In the example, the voltage is applied to the piezoelectric substance200 through two transparent electrodes 59, and thereby the piezoelectricsubstance 200 is deformed so that the function of a convex lens isexercised in FIG. 51.

The substrate 202 is previously configured into a convex form, and atleast one of the two transparent electrodes 59 is caused to differ insize from the substrate 202, for example, one of the electrodes 59 ismade smaller than the substrate 202. In doing so, when the appliedvoltage is removed, the opposite preset portions of the two transparentelectrodes 59, as shown in FIG. 52, are deformed into concave shapes soas to have the function of a concave lens, acting as the variablefocal-length lens. In this case, since the substrate 202 is deformed sothat the volume of the fluid 161 is not changed, there is the merit thatthe liquid tank 168 becomes unnecessary.

This example has a great merit that a part of the substrate 202 holdingthe fluid 161 is deformed by the piezoelectric substance and the liquidtank 168 is dispensed with.

The transparent substrates 163 and 165 may be constructed as lenses orplane surfaces, although the same may be said of the example of FIG. 50.

FIG. 53 shows a variable focal-length lens using two thin plates 200Aand 200B constructed of piezoelectric substances, in still anotherexample of the variable optical-property element applicable to theoptical system of the optical apparatus according to the presentinvention. According to this example, the variable focal-length lens hasthe merit that the thin plate 200A and the thin plate 200B, reversed indirection of the piezoelectric substance, are used and thereby theamount of deformation is increased so that a wide variable focal-lengthrange can be obtained. Also, in FIG. 53, reference numeral 204 denotes alens-shaped transparent substrate and 161 denotes a fluid. Even in theexample, the transparent electrode 59 on the right side of the figure isconfigured to be smaller than the substrate 202.

In the examples of FIGS. 51-53, the thicknesses of the substrate 202,the piezoelectric substance 200, and the thin plates 200A and 200B maybe rendered uneven so that a state of deformation caused by theapplication of the voltage is controlled. This is convenient becauselens aberration can be corrected.

FIG. 54 shows another example of the variable focal-length lensapplicable to the optical system of the optical apparatus according tothe present invention. A variable focal-length lens 207 of this exampleis constructed of an electrostrictive substance 206 such as siliconrubber or acrylic elastomer.

When the voltage is low, the variable focal-length lens 207 constructedas mentioned above, as depicted in FIG. 54, acts as a convex lens, whilewhen the voltage is increased, the electrostrictive substance 206, asdepicted in FIG. 55, expands in a vertical direction and contracts in alateral direction, and thus the focal length is increased. In this way,the electrostrictive substance 206 operates as the variable focal-lengthlens. According to the variable focal-length lens of the example, thereis the merit that since a large power supply is not required, powerconsumption is minimized.

The feature common to the variable focal-length lenses of FIGS. 47-55mentioned above is that the shape of the medium acting as a lens ischanged and thereby a variable focal length can be obtained. Suchvariable focal-length lenses, in contrast with those in which therefractive index is changed, have the merit that a variable focal-lengthrange or a lens size can be arbitrarily chosen.

FIG. 56 shows a variable focal-length lens using a photomechanicaleffect in a further example of the variable optical-property elementapplicable to the optical system of the optical apparatus according tothe present invention. A variable focal-length lens 214 of this exampleis designed so that azobenzene 210 is sandwiched between transparentelastic bodies 208 and 209 and is irradiated with ultraviolet lightthrough a transparent spacer 211. In FIG. 56, reference numerals 212 and213 represent ultraviolet light sources, such as ultraviolet LEDs orultraviolet semiconductor lasers, of central wavelengths λ₁ and λ₂,respectively.

In the example, when trans-type azobenzene shown in FIG. 57A isirradiated with ultraviolet light of the central wavelength λ₁, theazobenzene 210 changes to cis-type azobenzene shown in FIG. 57B toreduce its volume. Consequently, the thickness of the variablefocal-length lens 214 is decreased, and the function of the convex lensis impaired. On the other hand, when the cis-type azobenzene isirradiated with ultraviolet light of the central wavelength λ₂, theazobenzene 210 changes from the cis-type to the trans-type azobenzene toincrease the volume. Consequently, the thickness of the variablefocal-length lens 214 is increased, and the function of the convex lensis improved. In this way, the optical element 214 of the example acts asthe variable focal-length lens. In the variable focal-length lens 214,since the ultraviolet light is totally reflected at the interfacebetween each of the transparent elastic bodies 208 and 209 and air, thelight does not leak through the exterior and high efficiency isobtained.

FIG. 58 shows another example of the variable mirror applicable to theoptical system of the optical apparatus according to present invention.This example is described on the assumption that the variable mirror isused in the imaging optical system of the digital camera. Again, in FIG.58, reference numeral 411 designates the variable resistors housingvariable resistors; 414, the arithmetical unit; 415, the temperaturesensor; 416, the humidity sensor; 417, the range sensor; and 424, theshake sensor.

A variable mirror 45 of the example is constructed as a four-layerstructure in which the divided electrodes 409 b are spaced away from anelectrostrictive substance 453 including an organic substance such asacrylic elastomer, whose periphery is supported by the support 423, anelectrode 452 and a deformable substrate 451 are placed in turn on theelectrostrictive substance 453, and a reflecting film 450 including ametal thin film, such as aluminum, for reflecting incident light isprovided on the substrate 451.

The variable mirror, when constructed as mentioned above, has the meritthat the surface profile of the reflecting film 450 becomes smooth andit is hard to produce aberration, in contrast to the case where thedivided electrodes 409 b and the electrostrictive substance 453 areintegrally constructed.

Also, the deformable substrate 451 and the electrode 452 may be arrangedin reverse order. In FIG. 58, reference numeral 449 stands for a buttonfor changing the magnification of the optical system or zooming. Thevariable mirror 45 is controlled through the arithmetical unit 414 sothat a user pushes the button 449 and thereby the reflecting film 450can be deformed to change the magnification or zooming.

Also, instead of the electrostrictive substance including an organicsubstance such as acrylic elastomer, the piezoelectric substance such asbarium titanate, already mentioned, may be used.

Also, although what follows is said in common with the variable mirrorsapplicable to the optical apparatus of the present invention, it isdesirable that the shape where the portion of deformation of thereflecting surface is viewed from a direction perpendicular to thereflecting surface is long along the direction of the incident plane ofan axial ray, for example, elliptical, oval, or polygonal. This isbecause the variable mirror, as in FIG. 33, is often used in a statewhere a ray of light is incident at a grazing angle. In order tosuppress aberration produced in this case, it is desirable that thereflecting surface has a shape similar to ellipsoid of revolution,paraboloid of revolution, or hyperboloid of revolution. This s becauseit is desirable that in order to deform the reflecting surface of thedeformable mirror into such a shape, the shape where the portion ofdeformation of the reflecting surface is viewed from a directionperpendicular to the reflecting surface is long along the direction ofthe incident plane of the axial ray.

FIGS. 59A and 59B show the structure of an electromagnetic drivingvariable mirror applicable to the optical system of the opticalapparatus according to the pre-sent invention. FIG. 59B is a diagramviewed from the opposite side of a reflection film. Coils (electrodes)are provided to a deformable member to supply the current from a drivingcircuit and thereby electromagnetic forces are produced in the magneticfields of permanent magnets so that the shape of the mirror is changed.Since the use of thin film coils facilitates the fabrication of thecoils and reduces their rigidity, it is easy to deform the mirror.

FIG. 60 shows a conventional example of a Newtonian reflectingtelescope. In a telescope 345 of this example, light reflected by anobjective 344 is bent by an oblique mirror 317 so that a real image isformed at the position of an field stop 319 of a low-magnificationeyepiece 318 and can be observed through a user's eye 320. When ahigh-magnification eyepiece 321 is used instead of the low-magnificationeyepiece 318, a high-magnification observation at about the center ofthe field of view can be carried out. In the figure, reference numeral322 represents a field stop of the high-magnification eyepiece 321, andits size is smaller than that of the field stop 319 of thelow-magnification eyepiece 318. The low-magnification eyepiece 318 issuitable for high-magnification observation on the optical axis.However, when the low-magnification eyepiece 318 is used, there is theproblem that considerable coma is produced on the periphery of the fieldof view to impair the sharpness of an observation image.

Thus, as shown in FIG. 61, in a reflecting telescope 328 using thedeformable mirror 409 as the optical apparatus according to one aspectof the present invention, the deformable mirror 409 is used instead ofthe oblique mirror 317 to solve the above problem. Also, for thedeformable mirror 409, an electromagnetic or piezoelectric drivingvariable mirror is adequate because it can be changed into a convex or aconcave shape, but other driving ones may be used.

According to the reflecting telescope 328 of this example, when thelow-magnification eyepiece 318 is used, the thin film 409 a is deformedso that coma on the periphery of the image is reduced. Although thesharpness of the image at the center of the field of view is impaired,this drawback is invisible because of the low magnification, and afavorable image is obtained over the entire field of view. On the otherhand, when the high-magnification eyepiece 321 is used, the thin film409 a becomes planar and an image which is free from aberration and hashigh sharpness can be observed at the center of the field of view as inthe case of the conventional telescope 345 of FIG. 60. The deformablemirror 409 is driven by the driving circuit 304 so that aberration canbe changed in accordance with the replacement of the eyepiece.

When the deformable mirror 409 is used, like the reflecting telescope328 of this example, the sharpness of the image can be improved withrespect to the area of an image used by the user even in an observationapparatus which has a variable magnification function. Also, instead ofthe deformable mirror 409, the variable focal-length lens may be used.

FIG. 62 shows a microscope 329 using the variable focal-length lens 201as the optical apparatus according to another aspect of the presentinvention. In the microscope 329 of this example, the image of an object314 is magnified by a high-magnification objective lens 332 and isformed by a barrel lens 334 so that a real image is formed on a fieldstop 335. The real image is magnified through an eyepiece 336 and isobserved by a viewer. The high-magnification objective lens 332 can beswitched by a revolver 337 to a low-magnification objective lens 338.

In a conventional microscope, the barrel lens 334 is constructed withordinary lens elements, and thus aberration caused by a combination ofthe objective lens and the barrel lens in accordance with the lensreplacement fluctuates when the objective lens is changed. This does notnecessarily bring about the best imaging state.

In contrast to this, the microscope of this example is constructed sothat the refracting function of a ray of light of the variablefocal-length lens 201 is changed in association with a change of theobjective lens, and aberration due to the combination of the objectivelens and the barrel lens is corrected most favorably. Specifically, inthe microscope 329 of the example, when the area of an object to beobserved is changed, the variable focal-length lens 201 is driventhrough the arithmetical unit 414 by a driving circuit 341 in order tochange aberration of the variable focal-length lens 201 so that thesharpness of the image of the area becomes best.

Also, although aberration caused by combining the objective lens withthe barrel lens is controlled so that it is optimized, aberrationscaused by combining the objective lens, the barrel lens 334, and theeyepiece 336 may, of course, be controlled so that the variablefocal-length lens 201 is changed with respect to each combination andthereby aberration is optimized.

In the above description, reference has been made to the case of anobservation by the naked eye, but even in the case where the microscopeis combined with a film camera, an electronic camera, or a TV camera,aberration can be likewise optimized.

In the microscope 329 shown in FIG. 62, a path switching mirror 339 ismoved from the optical path to the left side of the figure and therebyphotographing can be performed by a TV camera 342. In this case,aberration caused by a combination of a lens 343 of the TV camera, thebarrel lens 334, and the objective lens is optimized by the variablefocal-length lens 201 and thereby more favorable photographing can becarried out.

As mentioned above, in the optical apparatus in which optical units,such as a plurality of objective lenses, the eyepiece, and the barrellens, are combined and used, aberration fluctuating due to eachcombination is optimized by changing the variable optical-propertyelement like the variable focal-length lens 201, and thereby thesharpness of the image can be improved. In this example also, instead ofthe variable focal-length lens 201, the deformable mirror 409 may, ofcourse, be employed.

Finally, the definitions of terms used in the present invention will bedescribed.

The optical apparatus refers to an apparatus including an optical systemor optical elements. The optical apparatus need not necessarily functionby itself. That is, it may be thought of as a part of an apparatus.

The optical apparatus includes an imaging device, an observation device,a display device, an illumination device, and a signal processingdevice.

The imaging device refers to, for example, a film camera, a digitalcamera, a digital camera for PDAs, a robot's eye, a lens-exchangeabledigital single-lens reflex camera, a TV camera, a moving-picturerecorder, an electronic moving-picture recorder, a camcorder, a VTRcamera, a digital camera of a mobile phone, a TV camera of a mobilephone, or an electronic endoscope. Any of the digital camera, a carddigital camera, the TV camera, the VTR camera, a moving-picturerecording camera, a digital camera of a mobile phone, and a TV camera ofa mobile phone is an example of an electronic imaging device.

The observation device refers to, for example, a microscope, atelescope, spectacles, binoculars, a magnifier, a fiber scope, a finder,or a viewfinder.

The display device includes, for example, a liquid crystal display, aviewfinder, a game machine (Play Station by Sony), a video projector, aliquid crystal projector, a head mounted display (HMD), a personaldigital assistant (PDA), or a mobile phone.

The illumination device includes, for example, a stroboscopic lamp forcameras, a headlight for cars, a light source for endoscopes, or a lightsource for microscopes.

The signal processing device refers to, for example, a mobile phone, apersonal computer, a game machine, a read/write device for opticaldisks, an arithmetic unit for optical computers, an opticalinterconnector, or an optical information processor.

The image sensor refers to, for example, a CCD, a pickup tube, asolid-state image sensor, or a photographing film. The plane-parallelplate is included in one of prisms. A change of an observer includes achange in diopter. A change of an object includes a change in objectdistance, the displacement of the object, the movement of the object,vibration, or the shake of the object.

An extended surface is defined as follows:

Any shape such as a spherical, planar, or rotationally symmetricalaspherical surface; a spherical, planar, or rotationally symmetricalaspherical surface which is decentered with respect to the optical axis;an aspherical surface with symmetrical surfaces; an aspherical surfacewith only one symmetrical surface; an aspherical surface with nosymmetrical surface; a free-formed surface; a surface with anondifferentiable point or line; etc. is satisfactory. Moreover, anysurface which has some effect on light, such as a reflecting orrefracting surface, is satisfactory. In the pre-sent invention, it isassumed that such a surface is generally referred as to the extendedsurface.

The variable optical-property element includes a variable focal-lengthlens, a variable mirror, a deflection prism whose surface profile ischanged, a variable angle prism, a variable diffraction optical elementin which the function of light deflection is changed, namely a variableHOE, or a variable DOE. The variable focal-length lens also includes avariable lens such that the focal length is not changed, but the amountof aberration is changed. The variable mirror includes a mirror suchthat the focal length is not changed, but the amount of aberration ischanged. The variable focal-length lens includes a mirror provided witha reflecting surface, a variable focal-length mirror whose shape is notchanged, or a deformable mirror whose shape is changed. In a word, anoptical element in which the function of light deflection, such asreflection, refraction, or diffraction, can be changed is called thevariable optical-property element.

In the present invention, an optical surface constituting the extendedsurface of the variable optical-property element, that is, an opticalsurface having the function of light deflection, is formed by thedimension that a light beam is not divided due to the difference of theposition where a ray of light passes with respect to the light beam ofthe object.

An information transmitter refers to a device which is capable ofinputting and transmitting any information from a mobile phone; astationary phone; a remote control for game machines, TVs,radio-cassette tape recorders, or stereo sound systems; a personalcomputer; or a keyboard, mouse, or touch panel for personal computers.It also includes a TV monitor with the imaging device, or a monitor ordisplay for personal computers. The information transmitter is includedin the signal processing device.

1. An optical apparatus comprising: an optical system comprising aseparable partial optical system; a variable optical-property elementarranged in the optical system, a ray-deflecting function of thevariable optical-property element being changeable itself; a drivingcircuit for driving the variable optical-property element; and anarithmetical circuit, wherein the ray-deflecting function of thevariable optical-property element is changed in accordance with a changeof an object area corresponding to an image to be used so thataberration of the optical system caused by the change of the object areais compensated for.
 2. An optical apparatus comprising: a variablemagnification optical system comprising a separable partial opticalsystem; a variable optical-property element arranged in the variablemagnification optical system, a ray-deflecting function of the variableoptical-property element being changeable itself; a driving circuit fordriving the variable optical-property element; and an arithmeticalcircuit, wherein the ray-deflecting function of the variableoptical-property element is changed in accordance with a magnificationchange of the variable magnification optical system so that aberrationof the variable magnification optical system varied in accordance withthe magnification change is compensated for.
 3. An optical apparatuscomprising: an optical system comprising a combination of a plurality ofoptical units; a variable optical-property element arranged in one ofthe plurality of optical units, a ray-deflecting function of thevariable optical-property element being changeable itself; a drivingcircuit for driving the variable optical-property element; and anarithmetical circuit, wherein the plurality of optical units areindependent of one another, and wherein a ray-deflecting function of thevariable optical-property element is changed in accordance with a changeof the combination of the optical units so that aberration of theoptical system varied in accordance with the change of theray-deflecting function is compensated for.
 4. An optical apparatuscomprising: a variable magnification optical system comprising acombination of a plurality of optical units; a variable optical-propertyelement arranged in one of the plurality of optical units, aray-deflecting function of the variable optical-property element beingchangeable itself; a driving circuit for driving the variableoptical-property element; and an arithmetical circuit, wherein theplurality of optical units are separable from one another, and wherein aray-deflecting function of ray deflection of the variableoptical-property element is changed in accordance with a magnificationchange of the variable magnification optical system so that aberrationof the variable magnification optical system varied in accordance withthe magnification change is compensated for.
 5. An optical apparatusaccording to claim 1, wherein the optical apparatus is an observationapparatus.
 6. An optical apparatus according to claim 1, wherein theoptical apparatus is a telescope.
 7. An optical apparatus according toclaim 1, wherein the optical apparatus is a microscope.
 8. An opticalapparatus according to claim 1, wherein the variable optical-propertyelement is a variable focal-length lens.
 9. An optical apparatusaccording to claim 1, wherein the variable optical-property element is avariable mirror.